HP 25 Owner's Handbook Manual

"The

success

if

we

offer

and

provide lasting value,

variety

of

and

our

customers superior products

useful

prosperity

services, both

of

and

Statement

our

company

that

before

are

supported

and

of

Corporate

will

be

assured

that

fill

real

after

sale."

Objective

Hewlett-Packard

only

needs

by a wide

s.

When Messrs. we

offered

offer

more

some

aT

Since

we

over

700,000

astronauts,

one

than

me

wOrla s

introd

mountain

Hewlett

world-wide.

and housewives.

of

our

Each to

solve

out a working

HP

calculators

(Cover

pocket

the

problems

lifetime.

background

superior

3,000

most

uced

our

and Packard

product

quality

alscernlng

first

Their

founded

, an

audio

products, designed

customers.

pocket

calculator

owners

climbers, businessmen, doctors,

calculators

its

owner

is

precision

can

expect

fill real needs. And they

courtesy

of

NASA)

our

oscillator.

include

crafted and

to

encounter

provide

company

and

in 1972,

Nobel

lasting

in 1939,

Today

, we

built

we've

sold

laureates

students

designed

through-

value .

for

, ,

HEWLETT

iJ PAC

KARD

HP-25

Owner's Handbook

August 1975

00025-90001 Rev. C 8175

Printed in U.S.A

©

Hewlett-Packard

Company

1975

Function Key Index

Manual RUN Mode. PRGM-RUN

FUnction keys pressed they are pressed.

Input

from

the

numbers

keyboard

and answers are displayed.

switch

execute

I

PAGM..aJ

RUN

individual

set

to

functions

RUN.

as

[@Fixed display.

Followed by a key , selects fixed point

(page26).

~

Scientific

Followed by a key, selects notation

(page

@@

Engineering display. Followed by a number engineering display

~

Prefix key. Press before to

select printed keyboard above function

(page13)

• Prefix key. Press

before

to

select printed

slanted face function (page13).

00

Mean. Calculates

mean (average) numbers

Ell

in

storage register

R,

(page

mJ

x Exchanges of X-and V-registers (page

37)

notation

scientific

display

27)

.

key , selects

notation

(page

function

in

gold

key

.

function

in

blue

of

key

totaled by

67).

exchange

contents

.

number

display

display. number

28).

key

on

the

key

on

of

the

y.

~

Percent.

x%

o Standard deviation.

Calculates standard deviation numbers

Ell

registers R3 R,

(page

mJ

down stack displayed X-register (page

00

Calculates of

the

display

EStore

number

by displayed storage specified. Followed by

arithmetic

key,

register (page

_Recall.

by

number

value

register

into X-register (Page

Calculates

of y (page

usi ng

totaled

in storage

through

68)

Roll

down

contents

for

viewing

36).

Reciprocal.

reciprocal

number

(page

. Followed

key , stores

number

register

performs

arithmetic

55)

.

Followed

key , recalls

from

storage

(0-7)

the

displayed

54)

.

by

.

. Rolls

of

in

in the

52)

.

in

(0-7)

operator

storage

specified

55)

.

5

[]

Summation

minus.

Subtracts

values

from registers R,

for

Ell

entries

Ell

Sums and V-registers storage registers R3

through

(page

PREFIX

I After

_

that

storage

R3

through

correcting

summation

(page

Summation

numbers

R,

66). I Clear prefix.

~

, •

or

mm

' cancels

key

(page

69)

. in into

,E,

50) .

.

I:mD Copies

number

in displayed X-register V-register

I3mIChange

Changes sign displayed exponent

(page

~

decimal for functions

I

REG

Replaces

storage registers Ro through (page

into

(page

16).

sig n.

of

number

of

10

14)

.

Degrees.

trigonometric

IClear registers.

degree

R,

56).

Sets

mode

(page

59).

contents

with

zeros

X-

or

of

BEnter

After numbers ex (page

~

radians trigonometric functions

[STK]

Replaces X-, Y-, Z-

egisters

r

(page

.Clear

the

register (page

~

grads trigonometric functions

ex

pressing, next

keyed in are

ponents

of

31).

Radians. Sets

mode

(page

Clear

stack

contents

, and T-

with

37)

.

x.

displayed

to

zero

15)

.

Grads.

Sets

mode

(page

ponent.

10

for

59).

.

zeros

Clears

X-

for

59).

ElElC8JEI

Arithmetic (page

[EJ

logarithm. Computes

natural (base of

X-register

~

Raises e

to

in

(page

~

logarithm.

common

(base 10)

displayed

(page

operators

16)

.

Natural

logarithm

e,

2.718 .

value in

displayed

(page

Natural

antilog

(2

.718 .

the

power

63).

logarithm of

63)

.

of

X-register

Computes

value

X-register

displayed

Common

..

)

63).

..

value

~

Common

antilogarithm

10-

to

the number X-register

~

Rectangular coordinate conversion. Converts polar

magnitude

angle

in X-and

registers

of

rectangular coord

inates

~

Polar conversion. Converts x, y

rectangular

coordinates

X-

and

in to

polar

and

angle

~

~[§]

cosine

, and

Calculate

or

cosine, value in X-register

I sin o' I

§J

Arc sine, arc

tangent. Calculate trigonometric function display

(page

~

Integer.

only

.

)

in

integer number X-register truncating portion

(page

I

FRAC I Fraction.

Leaves

only

portion

of

displayed X-register

by

truncating

portion

(page

. Raises

power

of

in

displayed

(page

63)

and

Y-

to

x and y (page

coordinate

placed

V-registers

magnitude

(page

62).

Sine,

tangent.

the

sine,

tangent

displayed

(page

59).

[t304]

arc

cosine

inverse

of

value in

59)

.

Leaves

portion

in displayed

by

fractional

51

).

fractional

number

integer

51).

[KJ

root displayed (page

.

0 of

number

X-register

~

V-register power in

the

X-register

62).

I

ABS

Gives the

val ue

number

I

.H

displayed hours

hours, minutes, seconds

(page

of

E!D

displayed

hours, minutes, seconds

,

decimal degrees

I

LAST

number before operation the

of

X-register

~

Pi.

of

pi (3.14159 into register

in

Computes

of

number

X-register

52).

Computes

in

displayed

(page

Raises

number

to

the

of

the

number

displayed

(page

I

Absolute

.MS I

Converts

X I Recalls

displayed

.

absolute

of

the

displayed

(page

Converts

decimal

or

degrees format

60)

.

value

format

hours

(page

displayed

the

Places value

...

(page

53).

square

in

square

53)

64) .

51).

to

in to

or

60).

into

49).

)

X-

.

in

H P-25 Memory

Automatic

T

Z Y

x{

0,00

0,

[J

G

Sign

,~+--

-

i.

-?

OFF.mmml

X3Y

hId

X;ty

OM

x=y

~

em

HEWLETT

Memory

,

Mantissa

~

,5

& 1 B . 2 S

ON

PRGM.mRUN

sin

cos

INT

FRAC

_H

II

I~II

IT

'+11

LAST X

I~I

·

PACKARD

I~I

'-LJI

+H.MS

" 0

Stack

}

5'''''''

Exponent

I

of

Exponent

10 sign of 10

} Display

I

Storage

tan

'~I

yx

ABS

'-LJl

PAUSE

Program

Automatic

Stop~

'~I

25

Reg

Ro

R 1 I

R2

R 3 I

~

R6

R 7 I I

;"e",

"M

5

-

I I

00 01 13 02 03 04 05 06

"

Registers

Memory

00

13

00

13

00

13

00

13

00

13

00

47

48

49

13

00

13

00

13

00

Programming Key Index

PROGRAM Mode

PRGM-RUN set

Function

recorded

memory. shows memory and (keyboard location function

Active

In

program

three

These keys can

recorded memory.

1

PRGM 1 Clear program. program

GTO 00 and resets

so

operations

at step 00

memory

switch

to

:

PRGM

0IIII

keys are

in

program

Display

program

step

the

number

keycode

row

in row)

key.

keys:

mode

keys are active.

in

program

Clears

memory

instructions

calculator

of

program

(page

RUN

and

of

only

not

to

begin

78).

the

be

Automatic RUN Mode

PRGM-RUN

set to:

Function recorded pressing from the keyboard. Input

and answers are displayed,

indicated.

Pressed keyboard:

1

PRGM calculator operations step 00 memory

1 RIS 1 Run/stop.

execution program. execution is

running

keys may be executed program

from

.1 Resets

so

begin

of

program

(page

78).

Begins

of

a stored

Stops

if

program

(page

PRGM.mIll

at

83).

switch

or

individually

Executed recorded instruction:

[R7SJ

program

(page

RUN

as

except

Run/

execution

83).

part

by

numbers

where

as

a

program

stop.

Stops

of

a

mI:J

Go to.

by

two-d

positions

to

that

of

program

No

instructions

executed

Followed

igit

calculator

step

number memory.

(page82)

6

nu';'ber

are

,

.

mI:J

Go to.

by a

two-digit causes execute instruction specified number

ntinue

co execution from

there

Followed

number,

calculator

the

at

the

step

program

sequentially

(page

to

87).

PROGRAM Mode

Active

keys:

mJSinglestep.

Displays step and

contents

program

(page 81).

1m

Displays step and co previous memory

(page

Back

ntents

81).

number

of

memory

step.

number of

program

step

Automatic RUN Mode

Pressed from Executed as a keyboard: recorded program

mJ

Single

keycode

program

step

executes

step

when

(page

Back

step.

keycode

program

step

displays

contents

when

(page

on

the

execution

step.

number

of

when

displays

92).

number

of

when

are

keyboard

Displays step and current memory pressed; instruction, result, and moves next r,

eleased

1m

Displays step and previous memory pressed;

original

X-register released. No instructions executed

Any key. Pressing any key stops program.

instruction:

to

I

PAUSE

of

Stops execution and of

93).

resumes execution

~§II1C=yl~

of

a

1@~lx=ol~

Conditionals. tests against

-register indicated. If true,

calculator

instruction program If false, next step

I

NOp

Calculator no continues

execution with the

memory

(page 94).

I Pause.

program

for 1 second

displays

X-register,

program

(page

va

lue in

that

or 0 as

executes

memory

calculator

(page

l No

operation.

operation

program

seq

the

instruction

contents

then

Each

x-register

in Y

in

and

uentially

7

84).

step.

skips

90).

in

The HP-25 Means Painless

Programming

Your

HP-25

is

a versatile, handheld

the

uses answers modes

•

That's quence lator.

prior H P-25 calc

To

problem manually,

and

powerful

to

:

Manual

toughest

the of

functions available to

quickly and easily. Programmed

sequence and

then

you wish to solve a

all

there

of

manual

You

can

computer

ulator

see

the

close

and a

and

others

like it.

Manual Problem Solving

To

calculate

can

be

used,

3.1415 ... , and

Ganymede, one miles.

To

Ganymede First,

the Then

bB!33

use the H P-25 to manually , you

slide the

PRGM"

press Display

~bH

II

!±}

Hewlett-Packard

complex

problem solving.

of repeats

the where: A

RUN

mathematical

You

of

problems, choosing

problem solving.

up to

49

different functions as you

that

sequence

particular

is

to

it!

A

pr

ogra

keystrokes

then

execu

programming experience

prog

relationship

programmed

then

use a

surface

d

is

the

of

Jupiter

can

press

calculator

switch

1

3200.

=

110240000.00

te the

rammin

between

program

area

of a sphere,

is

the

surface

diameter

's

12

the

OFF"ON

to

RUN.

~

--

that

g.

solution ,

9

calculate

m

is

progr

of

the

moons

following

1

electronic

logic

problems

work

from

The

automatically

type

is

nothing

remembered

am as

the manual solution to a

let's

to solve the

area,7r

sphere.

, has a

switch to

Di a

meter

Square

calculator

system

step-by-step

the

H P-25

of

often

the formula A =

compute

keys

to

in

either

among

the

correct answer

memorizes

press

problem.

of

as often as

more

than

by the calcu-

as

you like.

is

necessary

solve a problem

same

is

the value

diameter

the

in

order:

ON,

and

of

Ganymede

the

diameter.

compute

through

problem

of

dozen

them,

a se-

7r

of pi,

of

3200

area

slide

that

two

No

for

d

of

.

s

a

2

10 The HP-25 Means Painless Programming

II

f±!} [ 3.14 [

~

r[

3

:'.:2;";1=::6""99::C

="8C=:.7="8:===i,

O

Programmed Problem Solving

If

you wanted the surface areas

repeat

you could might wish to write a sphere from its diameter , instead

each

moon.

To

calculate

write

first the calculator, and finally you the answer.

Writing the Program: nothing more than the series to solve the

Recording the Program: gram into the calculator:

I.

Slide the

(program).

2. Press

Press

3. ing a program, the display gives you information will find l/seful later , but you now.)

the above procedure

the

area

the program, then you must

same

PRGM-RUN

PRG..,

II

a to clear the calculator.

the following keys

The

quantity

Area

of

program

of

a sphere using a program, you should

You

have already written

problem manually.

of

To

record the

switch

in

7To

Ganymede

of

each

that

would calculate

of

run

the program to calculate

keystrokes

order. (When you are record-

can

in

of

Jupiter

12

times .

pressing all the keys for

record

the program into

you would

keystrokes

PRGM~RUN

ignore the display for

square miles.

's

12

moons,

However,

area

it!

A program

execute

of

the

to

PRGM

that

you

of

pro-

you

a

is

II

:}

H3

~

Running

PRGM

.wmJ!J

~

bB bB

These

keys are the same keys you pressed to

solve the problem manually.

the

RUN

Program:

back

to

RUN

Slide

the

and press

PRGM-RUN

in

order

switch

Now

all

you

in

the

value

When

you

is

automatically

same

answer

For

example,

The HP-25 Means Painless Programming

have

to do to

for

its

press ~ the

executed

you

to

calculate

diameter

would

calculate

and

sequence

by

the

have

obtained

the area

the

area

press

of

keystrokes

calculator

of

Ganymede:

of

any

the~

, giving

manually:

sphere

(run /

you

is

stop)

key.

recorded

you

11

key

the

any

Jupiter

Display

13200. 1

32169908.78

program

of

Jupiter

You

key

in

then

press 's

you

the

moon

Press 3200

~

With area

of

its

diameter.

mode and compute,

area

of

Press Display

231

0

~

1

16763852.56

For

the

diameter

3220 miles:

Press

moons

1950~

3220~

Programming a

series

of

the~ key.

The

early manually use gramming, programming. or

programmed

look

at

this

that

makes

HP-25

features

the

simple

as

have

some

Europa, diameter

Display

1

11945906.07

1

32573289.27

the

HP-25 is

keystrokes

portions

the

power

you

will find a

Even

large

handbook

simple

that

power

of

700,000

1

Square

have

recorded,

's

moons-in

have

only

to leave the

diameter

~.

10

For

with a

1

of

example

Square

Area Area

that

easy!

then

handbook

of

the

HP-25;

executes

of

and

this

complete

if

you

have

used computers, .

It

explains

answers

make

your

out programming painless. Hp-25

, you'll

HP

calculator

miles.

you

can

fact,

of

any

calculator

each

sphere

, to

compute

diameter

of

miles.

1950

miles, and Callisto,

of

Europa

of

Callisto in

The

calculator

them

show

you

while in

guide to HP-25

other

you will

the of

want

unique

complex

become

owners

now

calculate

sphere-using

that

you

the

2310 miles:

in

square

remembers

when

you

how

easy

section

calculator

pocket

calcula

to

take a good

HP

logic

problems, and

When

an

apostle

before you.

in

RUN

wish to

surface

miles.

press

it

is

5,

Pro-

system

you

the

to

tors

see

just

Section 1

Getting Started

Your

HP-25

is

You

can

begin using

the

cord and plugging the your HP-2

tery for 6 or

from

power

be

in

the calculator.

To

begin:

• Slide the

shipped fully

from the ac

charger

5 on

battery

hours

first.

supplied by the

PRGM-RUN

OFF-ON

your

adapter/battery

Whether

Display

With

the play two kinds

When

I

0.00

PRGM-RUN

that

you see when you turn the

of

information:

I.

You

2.

see numbers as you key them in.

You

see all intermediate and final

calculated.

you first turn the

I to show you that a

Keyboard

Most

keys

on

the

tion

is

indicated by the symbol on the flat face by the blue symbol on the slanted key face, gold symbol written a

•

To select the function printed

the key, first press the blue prefix key function key.

•

To

se lect the function printed on the flat face

press the ke

•

To select the function printed

press the gold prefix key , then press the function key.

keyboard

bove

y.

assembled,

calculator

into an ac outlet.

power

alone, you should charge the bat-

you

operate

charger

switch P!lGM

switch

OFF~ON

set

to

calculator ON, the display is

ll

zero s are present there.

perform three functions.

the key on the

in

13

including a

immediately by

charger

, the battery

RUN,

calculator

blue on the slanted face

in

gold

to the

If

you want to use

from

battery

mil

RUN

to

ON.

the bright red dis-

ON

answers

of

the key ,

and

calculator

II

, then press the

above

must

a third by the

the key, first

battery

connecting

calculator

power

always

RUN

.

gives you

as they

of

set

One

func-

another

case

the key,

are

.

to

of

14

Getting Started

In this

handbook

appropriate

color

, the

selected

(either gold

To execute this function, first

press , then press

To place this number into the

II

' then press

pressH3'

display,

To execute this function, first

press

key function will

or

blue), like this:

appear

[CJ

Ej3.

EH'

~

in

.

the

Keying

Key in

as though you

point For

Key in 148.84

by pressing

The

in

numbers

must

be

example:

resultant

Numbers

by pressing the

were

writing

keyed

in

if it

the

keys

number

148.84 is

number

on

a piece

is

part

Display

1148.84

Negative Numbers

To

key in a negative

then

press

6mI

(-)

minus change

Press Display

6mI

You ber

in

now

Press Display

6mI

Notice

sign, will a

the sign

1

-148.84

can

change

the display.

in

the display

1 148.84

that only negatiye numbers are given a sign

number

(c

hange

of

the

sign

For

example, to change the sign

back

, press the

sign).

ppear

in

number

of

either

to positive:

The

now

keys in

of

paper.

of

the

number.

seen

in the display.

keys

number, preceded

the

display.

in

the

display:

a negative

or

sequence,

The

decimal

for the

For

number

example,

a positive num-

ofthe

- 148.84

in

the display.

just

,

by a

to

Getting Started 15

Clearing

You

can

clear

any

ram

(clear x).

This

numbers

key

that

erases

are

in

the display by pre ssing

the

number

in

replaces it with 0 .

Press Display

_ 10.00

If

you m

ake

number string by pressing

~

a mistake while keying in a

ED.

Then

key

number, clear

in

the

Functions

In spite board, you will find single, all-encompassing rule: When you press a

the calculator that

key.

of

the

dozens

immediately exec

of

function s avai lable

the

calculator

simple to

operate

utes the f un ction written

on

the

display and

the

correct

the

HP-25 key-

by using a

function

entire

number.

key,

on

Pressing a mealalelY

For

example,

Press

148.84

a

~

To

sq ua

re

Press Display

iii

[ZJ

~

and

[ZJ

keys

that

HP-25

operate

function

perrorm

to calculate

Display

1

148.84

1

148.84

112.20

the result:

1

12.20

1~1~48~.8~4==i

are examples

execute

upon

(except for statistics later).

Function two

keys

numbers.

key causes

mal

asin

either

keys

operate

runcllon

the

of

one-number

the calculator

.

square

gle number. A

one

numb

er

like

BJ

and 0

upon

either

root

of

148.84 merely:

function keys ;

ll

function keys

or

two

numbers

-more

one

number

to

im-

that

is,

in

the

at

a time

about these

or

One-Number Functions

To

use

I.

2. then

For exa key

in

To

calculate

anyone-number

Key

in

the

function

the

function

number

1/4,

number.

use

Press

mple, to

the

function

key

key) .

the

one-number

represented

key

in 4

(the x-number)

(or

press

by

key:

x,

then

the

applicable prefix

function

00

pr~ss

the

and

press

key, you

function

moo.

key

fir

key

,

st

.

Press

4

m

00

Now

try

these

ber

,first

key

25

vTsOO

5

10

..J

3204100 = 11790.00

log 12.58925411

71

2 =

Display

14. 1

4.

10.25

other

one

-number

in

the

number,

= 10.04

=

~15~0.~00

~====:

= 1100000.00

=

~11~.1~0~==~

L":

15:.::.

0

..:..

41

:.:..

.0

::.:

0~_-...-J

Two-Number Functions

Two-number bers

present

and

EJare

cannot numbers the

same

occurs

bers must

When before separate

functions

in

examples

add,

subtract

present

way

when

the

be

in

more

than

performing

the

two

are

functions

order

for

the

operation

of

two-number

, multiply,

in

the

as

calculator.

one-number

function

key

th e ca lculator be

one

number

an

operation,

numbers.

function

then

press

th e

(Use

that

to

be

function

or

divide

Two-number functions-that is

pressed. Therefore

fore

th e

ful1ctiol1 key

must

be

keyed

the

mm

problems.

funr:tion:

the

[iifl

must

ha ve

performed.

keys

unless

there

functions work

is,

the

into

the

key

Remem-

key

.)

two

[±)

because

are

oper

,

both

is presse d.

calculator

is u

sed

num-

G 0

you two

ati

on

nllm-

to

Getting Started 17

Use

the

must

function.

[fyou

key

To

place

operation:

I.

Key

2.

Pr

ess

3.

Key

4.

Pre

ss

For

example,

12

Imm

3

~

The answe Other

arithmetic

Imm

be

in

only

two

in

the

Imm

in

the

r,1

1S.00 I, is

key

keyed into

numbers into

fir

second

function key

you

The Separates The

I ne

whenever

one

numb

st

number.

to

separate

numb

add

12

first

second

tuncllon.

functions

calculator

you

the

first

er.

to

perform

fir

st

number.

displayed.

are

performed

more

never

calculator and

numb

the

er,

and 3 by press

number.

the

than

before

need

number

the

ing:

er

To perform Press Display

12-3

12

x 3

12

-;-

3 12 miim3

The

[LJ

key

numbers

th

When

s

hould

nated

at

2.

3.

4.

you

I.

to use

Key Pres

Key Perform

working

remember

by x on

is

also a two

powers

every

in

the

s miim

in

the

with any

the

1

2lmm3El

12

miim3 0 136.00 I

El

-num

, a

nd

you

other

two-number

first

number.

to

separate

second

number

operation

that

the

function

(press ,then

function

displayed

key symb

ber

can

the

use

first

(power).

1

9.00

14.

00

operation

it in

the

function

numb

key (includin

number

ols .

one

pres

to

press

from

operation.

from

the

same

1

.

It

is

same

key:

er

from

[LJ

).

is al

number

sing a

Imm

perform

the

second.

the

seco

way:

used

simple

the

second.

g 0

ways

to

).

desig-

.

an

nd.

raise

way

you

The

number

displayed

is

always x.

18 Getting Started

So,D means square root

I

. , etc.

displayed Thus,

number

to calculate 3

of

the displayed

6

:

number,[K]

mean s

Press Display

3

Imim

6 16.

o

N ow try the following problems using the 0 key, keeping

13.

00

1

6.

1729.00

X,

the displayed

The

answer.

number, is

now 6.

mind the simple rules for two-number functions:

4

16

812

(16 to the 4th power) = 165536. (81

sq uared) 16561.00

00

(You could also have done this as a one-number function

using 0 ·)

5

225

(Square root

of

225)

115.00

(You

also

could

have

done this as a one-number function by

usingD

16

2

16

25

(2

to the 16th power) = I 65536.00

(4th root

of

16)

,-

I 2_

.0

_0

__

-'

in

·)

Chain Calculations

The

speed and simplicity

Packard logic

culations.

form

only one operation

calculate-the

system

Even

during the longest

Hewlett-Packard automatic memory stack

stores up to four intermediate results inside the

you need them , then inserts them into the calculation.

of

operation

become

most

at

a time, and you see the results as you

of

the HP-25

apparent

of

calculations,

's

during chain cal-.

you

calculator

Hewlett-

still per-

until This

Getting Started 19

system natural paper,

For

If

would

You HP-25, one result

as

but

example,

you

were first

.

and

work

first

makes

Press

12

mmm

3

[±J

and

.

press

mmm

matically number.

To

the

it

would

the

calculator

solve

working

calculate

then

you

through

operation

...

Display

12

1

.

12

1

.00

3

1

.

1

5.00

then solve

to

sto

stores

it ins

continue.

process

be

if

(12 +

the the

would

~

the

at a time.

]

1

I

for

re

the

ide

of

you

(11

working

were

takes

care

3)

x 7.

problem intermediate

I

3t

IS-

mUltiply

x

15

X 7

problem

Intermediate

the

exactly You solve

(12 +

the

final an

intermediate

calculator

through a problem

working

with a pencil

of

result

it

the

x 7 =

the

intermediate

7=

105

the

for

3)

result

swe

r.

result-the

when

out hard

of

same

the

.

You

you

with

pencil

part.

and

paper, you

(12 + 3).

result

way

with

intermediat

don

't need

HP-25 auto-

key

in

the

and

by

7.

the

e

to

Press

7

Display

1

7.

1

05.00

The

intermediate ceding stored key

in

Pres

sing the new result

, givi

operation

ins

ide

the

this

number.

the

function

number and

ng

you

result

is a

utomaticall

calcula

key

the

final

from

the pre-

tor

when

multiplie

intermedi

answer.

y

you

s

ate

20 Getting Started

Now

try

these

problems. Notice that

have

to

press

mImm

to ins

lator-each subsequent number

and

an a

utom

ert a pair

operation

atically

stored

for

each

of

numbers

is

performed

intermedi

problem

into

using a new

ate

result.

you

the

only

calcu-

To solve

(2 + 3)

10

3 (16 -

14

+ 7 + 3 - 2

4

4)

Press

2

mImm

3

El

10

El

16

mImm

4

El

3

o

14

mImm

7

[±]

3

El

2

El

4

El

Display

I

0.50

136.00

1

5.50

Problems same ate and

that

simple ma

results. For exampl

paper, you

are

even

nner

would:

more

, using

e,

complicated

the

automatic stor

to

solve

can

be

(2

+ 3) x (4 + 5) with a

age

solved of

intermedi-

in

the

pencil

(2 + 3) x (4 + 5)

First

solve for the contents

parentheses ....

You

First

of

these

. and then you would multiply the

two intermediate

work

through the problem the

you solve for the intermediate result

Getting Started

answers

same

way

. .

..

and

then

these

parentheses

together.

with the HP-25.

of

(2 + 3)

.

21

for

~

x

(4+

5)

~

Then

add 4

and

5:

(Since you can rate the first

Procedure

~~

perform

must

now

a function, you use the miim key again

number

S- j

Then

multiply the intermediate

answer

:

Procedure

~X...(4

!J x

Notice mediate plied-the

1

5)-

'1

that

you didn't need to write

answers

from inside the parentheses before you multi-

HP-25 automatically sta

12. 1

1

pair

[±]

1'--

answers

1

Display

2.00

5.00

of

9_.0-'-0

_---'

together

45.00

down

cked

Press

2

miim

3

[±]

key

in

another

of

the pair from the second.)

Press Display

4 miim 5

Press Display

0

Intermediate

result.

numbers before you

to

.sepa-

for the final

or key

in

the inter-

up the intermediate

22 Getting Started

results

inside

the

calculator

last-in, first-out No

matter

be

reduced

work

through

use

if

you

For

example

basis

how

complicated a problem

to a series

the

problem

were

working

, to solve:

for

you

when

it

of

one-

in

it

with a pencil

(9 x 8) + (7 x 2)

(4

and

was

time to multiply.

and

two-number

the

same logical

x 5)

brought

may

look,

and

them

it

oper order paper.

out

can

alway s

ations.

you

on a

Just

would

Press

9mm:iD80 7

mm:iD

[±J

4mm:iD50

El

Now

try

you

would

mediate

Display

172 .

00

1

14.00

20

1

86.00

1

20.00

14.

30

these

problems. Remember

with a pencil

answers-they're

and

paper, but

I

ntermediate

Intermediate

(9 x 8)

Intermediate

The

final

ha

ndled

calculator.

Problems

(2 x 3) + (4 x 5) = 1'--

.J(2 + 3)

(,14 + 12) x (18 - 12) _

4 x (17 - 12)

x (4 + 5) +

(9 - 7) - L.C

.fI6.38

-,"---::-c=--- = 1

.05

X 5

.;-

(10 - 5) = 1'-4=

..j(6

+ 7) x

A Word About the HP-25

Now

that

you've

begin

to logic pa Polish

fully

system.

renthesis-free, unambiguous

Notation).

learned

appreci

With

how

ate

the

this

system, you

to

ben

method

use

efits

result

added

to

result

answer.

to

work

don't

worry

automatically

2_6_.0_0

_----'

r:[

:-:-::

7

8

O

-'C

o.::.

.

181.

00

.0

(8

+ 9) =

the

calculator, you

of

the

Hewlett-Packard

enter

number

called

of

(9

x 8).

of

(7

x 2).

(7

x 2).

of

(4 x 5).

through them

about

inter-

by the

-c:--

---,

-=-

0_ ----'

..:....0_----'

1L:2 ___

1._57_---'

s usin g a

RPN

(Reverse

as

can

Getting Started

It

is

this unique system vantages whether gram

or

using the HP-25 under manual control:

• You never ha time.

The

making them more complex.

• Pressing

You fewer keystrokes and less time spent.

HP-25

afun

work naturally through comp licated problems, with

that

you're

ve

gives you all these calculating ad-

writing keystrokes for an HP-25 pro-

to work with more than one function at.a

cuts

problems down to size instead

ction key immediately executes the function.

• Intermedi ate results app ear as th ey are calculate

are no ,. hidden" calculations, and you as you go.

can

check

23

of

d.

There

each step

• Intermediate results are automatically handled. You don't

have to write down long intermediate answers when you work a problem.

• Intermediat e answers are automatically inserted problem on a

remember

•

You

can calculate in the same order you do with pencil

la

st-in, first-out basis. You don' t have to

where

they

are a

nd

then summon them.

into the

and

paper. You don't have to think the problem through ahead

of

time.

The

HP

amply rewarded by the ease with which the HP-25 solves the longest, most complex equations. With few moments

system takes a few minutes to learn. But you'll be

HP

, the

in

of learning yields a lifetime

of

ves tment

mathematical bliss.

of

a

Section 2

Controlling the Display

In

the HP-25 , numbers to only which

app

two

decimal places.

is

ac

tually

ears in the display as

to show you the of

decimal places).

Although a

number places , the HP-25 always ber as a 10-digit mantiss a and a two-digit

example ,

when

you

two decimal place s:

Press Display

2 mm 3 0

However

c...:c1

, inside the calculator all

tiss as and two-digit exponents

calculates using full 10-digit numbers:

2.000000000 x

yields an a

You

these d

nswer

see only t t

.... , i_g_it_s_

. _. _.

in

the display normally

For

in

the calculator as 3.141592654, normally

number

is

normally shown to only two decimal

compute

6

"-".o-'-o_---'

example , the fixed

~

(unless you tell the

rounded to a greater

compute

s internally using

2 x 3, you see the ans

number

of

I O. So the calculator actually

00

10

mm 3.000000000 x

that

is

actually carried to

I 6.00

0000000

x10

oo

---~

__

-----'

appe

or

lesser

exponent

s have

10

digits:

l

.

..

but these digits

are also, present.

ar rounded

const

ant

calculator

number

each

num-

of 10.

wer

For

to only

digit man-

00

0

7T,

Display Control Keys

~

allow s numbers to be di splayed

ISCI I displays numbers

mat,

I

ENG

I displ ays numbers

of

10

shown

in

mUltiples

in

engineering notation, with

of

three (e.g. ,

Display control alters only the ma

displayed by any

of

the HP-25.

the display control keys.

The

actual

in

select, these rounding options affect the display

HP-25 always calculates internally with a full 10-digit

(multiplied by

10

raised to a two-digit exponent) .

in

fixed decimal point for-

scientific notation format, and

exponents

3

6

,

10

-

10

which numbers are

itself

is

not altered

what notation you

No matter

25

nner

number

10

in

9

) .

only-the

number

26

Controlling the Display

Fixed Point Display

Decimal point

Sign~

10-Digit

Fixed Point Display

Using

fixed

point

to

be

shown

0,

followed by a

decimal places (0-9) to which displayed cludes

trailing

l

ator

is

turned tation with the display example:

Press (Turn

the calcul

OFF, then

123.4567

[EJ

mmiD

4

07 00 02

display you

after

the decimal point.

numb

er begins at the left

zeros

wit hin

OFF,

then

ator

ON.)

number

the

ON,

rounded

Display

10.00 1

123.46

1

123.4567

1

123.4567000

1123. 1

1123.46 I

Number

can

key

the

display

setting

it "

to

specify

the

It

is

sel

ected

to specify

is

to

side

of

the

selected.

wakes

up "

two

decimal places.

Display

two

decimal ternally, however number original value

123.4567.

1 1

Normal

number

be

in

of

by

pressing

the

number

rounded.

display

When

the

fixed

point

is

rounded

places.

maintains its

of

FIX

2 displ ay.

places

The

and

calcu-

no-

For

off

In-

, the

of

in-

to

Controlling the Display 27

Scientific Notation Display

Sign

..

of

Exponent

,

of

10

(This

means

- 1.2345678 x

In scientific

to

digit ber

of multiplied ing

with

Scientific

number the

number

trailing

notation

the

left

digits (up to

by a power

very

notation

key

to

is

zeros

Press

123.4567 D D

In scientific

mum

[§] [§] [§]

mIim

2

4

7

notation, although

of

seven the full 10-digit nally.

The

rounding For

tific off

of

example,

notation

to

the

seventh

portion

the

Calculator

Eight-Digit

Scientific

of

the

decimal point followed by a specified num-

seven)

large

or

is

specify

rounded.

within

the

Notation

10

each

number

to

of

10.

small

numbers.

selected

the

number

The

display

selected

Mantissa

23

-

)

the

right

It

is

particularly

by

pressing

setting.

Exponent

Display

is

displayed

of

the

decimal point

useful

Dfollowed

of

decimal

is

left-justified and includes

For

example:

Display

02 02 02

the

calculator

point

two-digit

the

calculator

decim

Normal Display Display Displays

, it always

exponent

not

displayed

and

specify full scien-

al point:

1

123.46

1

1.23

11.

2346

1

1.2345670

digits

after

the

number

of

the

displayed

if you

key

decimal

and

the

number that is

portion.

in 1.000000094

display ( D @ 7),

digit

after

the

1.000000094

rounds

to

tJis

digit

in

SCI

of

10

with a single

and

when

work-

by a

places

to

which

FIX

2 display.

2

s 1.23 x

s 1.2346 x

1.2345670 x

•

10

2

10

displays a maxi-

maintains

of

10

inter-

affects

the

displ

ay

rounds

7.

•

2

•

28 Controlling the Display

Pres

s Display

1.000000094 1

a

[§QJ

7 1

In

SC

I 8, decim the

You

the

al

point, but you

decimal:

see

to

he re

Press

a

lli£L]

8 1

You

can

see that

so have caused

al after

the

decimal

display

I .0000000

...

if the to

1.000000094

1.0000001

would

round

can see only

94

~~

Display

1.0000000

you

had

key

display

a o ne ( I).

to round

00

off

.

00

ed in 1.0 00000095, SCI 8

Engineering Notation Display

First Always

Engineering nota ponents often Thi

s is particularl y u tion s , w h thre

e.

ere

units of measure

See

the

prefix chart

Specified

Three

Present

Engineering

tion all

that

are

sef

Digits

multipl

ul

Notation

ows all

in

sc ientific a

below.

Digits

Exponent a

numb

es

of

are

often spec

Multiple

thr

to

the

eighth

out

to

but

the calcul

r

ounds

the

seve

of of

Display

ers

to

be shown

ee

(e.g., 10:l,

nd

engineering cal

ifi

digit a

seve

n digit s

to here

nth

and

Ten Three

ed in

fter

after

ato

r displ

in

SC

I 8.

wou

fin

al dig

Always

with ex-

10-

li, 10").

cula-

multiples of

the

ay

ld

it

Multiplier

'2

10

9

10 10

'

3

10

3

10-

10-'

9

10

-

12

10-

15

10

-

18

10

-

Prefix

tera giga mega kilo milli micro

nanD

pico fe

mto

atto

Symbol

T

G

M

k m

}J.

n

P

f

a

Controlling the Display 29

Engineering

a

number

always

additional

Press

notation

key. In

engineering

present, and

digits

displayed

Display

is

the

0.0000123451 0.000012345

a~O

a

~

Notice greatest neering

2

that

because

number

notation

112.3

1

12.345

rei

1

:-;2;-;.3;;-;4~50-;:-:

0

=----

the

of

additional

is

five.

Press Display

I

12.345000

'I

-:-12=-.-=-347.5::-:0:-=0-=-

0- -

1 12.345000

Rounding to

the As not lator, but

When

shifts to maintain ample causes

exponent

Press

a

~

100

of

displayed

rounding

with

all

affect

display

the

only

engineering

to

show

the

, mUltiplying

the

decimal

of

10:

o

I 12.3 LI.:.c12:::.c3::.:. ____

of

numbers

actual

alters

notation

the

mantissa

exponent

Display

numbers

formats,

number

the

manner

the

point

selected

by

notation, the

number

-06

after

the

I

Engineering

key

First

power

of

three

-06

IThe

number number yond

-:::-

06"'

1

first

three

digits

-061 Maximum displayed.

-=-06-:-11 No

-06

in

1No

in

SCI7

change change

ENG 5 and

engineering

as

it is

in

which

has

been

as

units, tens, or

of

10

as number to

-06

-0~6~1

shift

I

Decimal

now

to

the

remains

pressinga~

first

specifies

first

three. For

notation

three

digits

of

lOis

the

.

key

of

digits

the

first

three.

are

can

always be

that

number

in

display.

in

display

and

SCI8,

notation

held

internally

the

number

selected,

hundreds

a mUltiple

in

the

right

without

point

shifts.

6

at 10-

followed

three

digits

the

number

example:

display.

visible

and

proper

specifies

displayed

present,

specified

of

digits

.

ENG

6 is

discussed

display by

the

is

displayed.

the

decimal

of

three. For

calculator

altering

Powerof

•

by

are

of

mUltiple

the

.

be-

the

in

engi-

similar earlier.

does

calcu-

point

in

order

ex-

by

10

the

10

30 Controlling

However, to

another

units

multiplying again by

multiple

position:

Press

100

Display

I

1

:..:.::.-23"--

L

the

of

__

Display

three

-

=c

:o.-J1

03

and

Decimal

I 0 shifts

10

the

causes

decimal

point

to 10-:).

Automatic Display Switching

The

HP-25 scientific too

small

keeps

you

For

example

answer

the

Press

D

!£iKJ

2

-

.051mmJ

3D

CZl

Another normal played

.

After

automatically

new

number

matically selected

The

H P-25

too

large

switch

from

switches

notation

to

be

from

, if you

is

1

1~0=.0=0~==~1

1 0.

1

way

FIX 2 display,

reverts

.

also

(>

1010)

fixed if

the

display

(SC

I 7)

seen

with a fixed

missing

automatically

unexpectedly

try

to

Display

0.00

05

1.2500000-04

of

displaying

is

switching

keyed

back

switches

for

fixed

you

00

you

in

to

solve

from

whenever

solve

shown

1

the answer

would

or

_ is

the

to scientific

point

fixed

the

number

decimal

large

(.05)3

in

normal

in

scientific

ENG 0 from Normal

Display automatically

to

1582000 x 1842:

FIX 2 display.

SCI 7 to

would

have

seen

from fixed to scientific,

pressed

fixed

point

notation

display. The

the

exponent

point

to

shifts.

point

notation

is

point.

or

small a

FIX 2 display

notation:

answer.

be 0.000125,

only

the

display auto

display

if the

display

move

Power

too

This

nswer

example.

switched

I

0.00

originally

answer

to

shift

to

the

of

to full

large

feature

but

I dis-

when

will

not

or

s.

,

in

a

-

is

Press Display

1582000 1842 0 1

However, large scientific

ImIm

for

"11'---5~82"-0-0--'-0.-'-0-0-~

if

you

fixed

point

notation:

2914044000.

multiply

notation,

the

1

Fixed

result

and

decimal

by 10,

switches

point display.

the answer

automatically

is

too

to

Controlling the Display

31

Press

Notice notation

must

that

be

selected

display

Keying

You

can

key

D (enter

'2

(15.6 X

Press

15.6

10

D

12

Now

Press

mum

25~

You

can

save

pressing

example,

Press

6

D a nd

key

mum

52

EJ

To

see

your

Press Display

a

@Cil

6 1

Display

1

2.9140440

automatic

modes

from

the

in

Exponents of Ten

in

numbers

exponent

),

answer

and

multiply it

Display

1

15.6

1

15.6

115.6

Display

11.5600000 1

3.9000000

time

when

then

in

I million

Display

IL

1_.

___

rI1:-. ---

LI

-'-.10:...:0:...::0.=.0,,-00:.:.

'I 1:;";9;-;;2-;;-30:;:-

in

1.923077

often).

scientific

10

I Scientific

switching

mUltiplied

keying

pressing

is only-engineering keyboard.

For

example,

by

25:

00 12

I

(This means 15.6 x

13

1

14

I

in

exact

the

(lOB)

and

divid e

--'0-'-0-.J1

You number I before pressing

D

exact pow

0

::-::

6-'1

,,-00=---

-,1

Since scientific answer notation

--,

notation

04

mum.

1

.:;:77

:;--

notation

between

by

desired

fixed

and

notation

powers of

powers

by

do

when

you

with six decimal places:

1 0

by

to

key

in

15.6 trillion

of

10

power

52.

not hav e to key

the

numb

er

of

10.

have

not

notation

revert

s to fixed point

when

YOLl

display.

scientific

display

pre

ss ing

'2

10

.)

by merely

of

10. For

in

er

is

an

spec

ified

, the

press

the

32 Controlling the Display

To

key

in

negative

a ,

pressEml

power

of

10.

roughly, 6.625 x

expone

to make the

For

example

27

10

-

erg sec .

nts

, key

of 10, key

exponent

in Planck's

-and

in

the

number

negative, then key

constant

multiply

it

by 50.

, press

in

the

(h)-

Press

B3

~

2

6.625a

lmJ 1

27

Imim

500

thea

Using mantissas and two-digit use the a key, the

Display

1

0.000000

10.00

16.625

6.625 625

16.

16.6250000 1

3.3125000

key, you can key

exponents

H P

-25 di

digit mantissa and a two-digit number

key

may have to be altered slightly

it

in

using

thea

• If you key

key:

in a number eight digits to the left overridd

the

digits

theDkey. (Thus

as 12345678.91 x

• If you key

afte

not

rectly, begin again

it

en

and

number

or

does not operate . Begin aga

in

a form th at display s the mantissa with eight

less to the left

10

in a number

r the first eight digits

oper

ate upon

that

and

s first sign

ifi

cant

digit

, 123456789.1 x

of

24

. )

display, then proceed using

55

x

10

cannot be keyed

as 0000.00025 x

10

5

4,

or

00

1

I

001

- 00 1 27

1

-

-27

1

Er

g sec.

- 251

in

num bers made up

of

10.

However,

splays each

exponent

whose manti s

number

of 10. I n a few cases, a in

form before you can

sa

contain

the decim al point, the D key

of

the decimal point

whose

of

the display,

number.

place the

is

one

of

thee

in

that

as 0.000025 x

23

10

could be keyed

first significant digit

To

key

in

number

in a form such

the first eight digits

key. (Thus, 0000.000025

form.

It

could be keyed in

5

10

bef

theD

the

5,

for

in

of when

as an eight-

s more than

and key

ore pres

number

example

10-digit

occurs

key

of

you

is

in

sing

in

does

cor-

that

the

.)

-,r:l.11

n~lIcn

IVlnt-t-l

Calculator Overflow

When

the

x

has

(1

10

x

number

99

,

the

exceeded

49

10

X

)

in the display would be

HP-25 displays all

the

calculator's

(1

x

1050),

the

HP-25 will display

Controlling the Display 33

greater

9's

to indicate

range.

For

than 9.9999999

that

example,

the

problem

if you

answer:

solve

Press

m:l49mIim

50

m:l

0

But

if

you

Display

1

1.0000000

1

1.0000000

attempt

49 99

to multiply the

above

result by

HP-25 display indicates overflow by showing you

Press Display

1000

A display ofl OF lindicates

re

gis ters

description

1

has

overflowed.

of

the HP-25

9.9999999

99

that

See

section

storage

one

of

registers.

the

calculator's

4,

Function

Error Display

If

you

ap

will For

example

as an

Press

ImIim

08

You

can

number

happen

pear

improper

to

key

in

an

in

the display.

improper

operation,

, try to divide 1 by 0 (the H P-25 will recognize this

operation):

Display

1

.00

I

Error

clear

the

error

by

into

the

displayed

pressing

X-register.

ED

or

by keying

100,

the

aIl9's:

storage

Keys,

for a

the word Error

another

Press Display

ED

All

t?ose

are listed

~Io_.o_

o

______

~perations

In

appendix

th at

B.

cause'

~

l

-=

Er-r-o-r

-'

1 to

appear

in

the display

Section

3

The Automatic Memory Stack

The Stack

Automatic storage HP-25 slides so easily through the most complex equations. And automatic storage automatic memory

Initial Display

When you first switch the calculator ON, the display shows

1 0.

00

I.

This

register. Basically, numbers are stored and manipulated

"registers." or

5)

or

how many (e.g. , 3.141592654, -

27

\0

),

x

The

one form the automatic memory Y, the displayed X-register on the bottom. When the calculator switched

occupies

displayed X-register, which

of

four registers inside the calculator that are positioned to

Z, and

T.

ON,

of

intermediate results

is

made possible by the Hewlett-Packard

stack

.

represents the contents

Each

number, no

one

entire register.

matter

stack

They

are"

stacked"

is

the reason

of

the display,

how few digits (e.g., 0,

23

.28362,

the only visible register ,

. We label these registers X,

one

on top

of

these four registers are cleared to 0.00.

that

in

the machine

or

2.87148907

the

other

or

the

X-

with

1,

is

Name

T

Z

Y

X

Register

0.00

Always displayed.

Manipulating Stack Contents

The m (roll down) and

review the computation

stack

at

any time.

l!'D(x

contents

or

to shift

35

exchange

data

y)

keys allow you to

within the stack for

36 The Automatic Memory Stack

Reviewing the Stack

To

see how the m key

bers 1 through 4 by pressing:

The

numbers

and

its

Each

time you press the m key, the

one

ward

will be rotated around to the T-register when you press m .

that

contents

look like this:

register. So the last

works,

4

mmiD 3 mmiD 2 mmiD

you keyed

T

4.00

first load the

in

are now l

Z 3.00

Y

2.00

1.

X

Display

stack

number

that

stack

1

oaded

contents

you

with num-

into

the

shift down-

have

keyed

stack,

in

When you press the m key, the stack contents

. . . from this

T

Z

Y

X 1.

Notice ters

themselves

X-regi

Press . . . from this . . . to this

T 1.00 T 2.

...

4.00

3.00

2.00

Display

that the

ster

m again

contents

maintain their positions.

are always displayed, so I 2.00 I

and

of

the stack contents

.

T

Z

Y

X

the registers are shifted.

..

to this.

1.00

4.00

3.00

2.00

are

shifted

00

The

Z 4.00

Y 3.00

X 2.00

Display

are

rotated

Display

The

contents

is

now visible.

...

Display

...

regis-

of

the

The Automatic Memory Stack 37

Press

Kia

twice more

. . . through this . . . .

T

3.00

z

2.00

y 1.00

X

4.00

Once

again the

that

you know how the

to review the

contents

always tell what

that

it

takes four presses

...

and

the stack shifts

Display

number

1.00

is

in

stack

is

of

the

stack

is

in

the calculator. Always

ofthe

...

..

back to the

T

Z

y

X

4.00

3.00

2.00

1.00

start

Display

again.

the displayed X-register.

rotated, you can use the

at

any

time so

that

remember

Kia

key to return the

contents

Kia

you can

, though,

their original registers.

Exchanging X and Y

Thef!D and V-registers without affecting the Z- and T-registers. pressf!D

bers

. . . from this

Similarly, pressing X- and V-registers to their original places.

position numbers

(x

exchan

ge y) key exchanges the

with

data

intact from the previous example, the num-

in

the X- and Y -registers will be changed .

...

T

4.00

Z

3.00 Z

Y

2.00

X

1.00

f3D

in

the stack

again will

.

T

Y X

or

simply to view the V-register.

..

to this.

4.00

3.00

1.00

2.00

restore

contents

of

the numbers

This

key

is

the

If

in

used to

Clearing the Stack

To

clear

the displayed X-register only, press riD.

entire automatic memory stack , including the displayed

register , press in

the

stack

ON

, it "wakes

Although it may be comforting,

s

tack

or

the displayed X

lation.

This

in

the

stack

~

(clear

sta

ck) .

Thi

s replaces a

with zeros. When you turn the calculator 0

up"

will

with all zeros

become

obvious when you see how old results

-re

in

the stack regi sters .

it

is never ne

gister when startin g a new

are automatically lifted by new entries.

cessar

To

clear

ll

numbers FF,

y to clear the

cal

Now

key

to

X-

you

the

X-

then

cu-

38 The Automatic Memory Stack

Press

ID3

now

, and the

. . . from

T

Z

Y

X

You

mEl

If

you press

. . . from this

T

Z

Y

X

this.

. . .

4.00 T

3.00

1.00 00

verify

Display

that

the

2.

can

by using

0,

...

4.00

3.00

1.00

0.00

Display

stack

contents

..

Z

Y

X

only the X-register

m key to review

the

contents

of

. . . to this .

T

Z

Y

X

the the

The Key

When

you key a written main unchanged. 3 J 4.32,

into the displayed X-register

your

Name Register

T

Z

Y

X

In

order separate second.

One to change the

. . . from

T 0.00 Z 0.00

Y 0.00

X 314.32 Display

to key

the digits

way to

this.

number

For

stack

separate

contents

. . .

example,

registers would l

0.00

314.32

in a second

of

the first

numbers

of

into

the

calculator, its

if you

ook

number

is

to press

the registers

..

T 0.00

Z 0.00

Y 314.32

X 314.32

are

changed ...

to this.

4.00

3.00

1.00

0.00 contents

other stack

are

0.00

and

the

other

keyed

like this:

Display

at

this point, you

from

mmiD.

...

to this.

Display

are affected by

stack

contents.

changed

Display

contents

registers re-

in

the

number

the

digits

PressmmiD

Display

...

must

of

are

the

As

you

and

X.

·

..

T

Z

V

X

rD3

·

.. T

Z

V X

can

Y.

(The

T,

respectively, and

of

the

stack.

numbers

number, and

For

example, key

stack

registers

from this

0.00

314.32

replaces

then

example would

from this

0.00

314.32

543.28

into Z top different

Immediately

for a new

in the

number

For

you

see,

the

numbers

But

in all

after

...

Display

any

writes

, if

you

pressrD3

...

Display

The Automatic Memory Stack 39

number

pressing

change

number

over

had

in Y

this will

four

that

in

the

...

the

meant

now

to

in

the

displayed

and Z have

the

number

be

more

registers .)

mum

,

new

number

.

..

T

Z

V

X

in

the

display

zero

in X.

to

key

change

the

.

..

T

Z

V X

also

in T has

apparent

the

X-regi s

writes

543.28

to this.

0.00

314.32

543.28

with

in 689.4

stack ...

to this.

0.00

314.32

0.00

X-register been

been

over

and

Display

zero.

instead

Display

is

copied

transferred

lost

when

we

ter

is

prepared

the

number

the

contents

Any

of543

off

to

the

have

of

new

.28,

and

then

·

..

T

Z

V

X

Notice is

keyed

ever,

keyed

key

from this

0.00

314.32

0.00

that

in

the

numbers

in

immediately

in

689.4 to

...

Display

numbers immediately

in

the

after

change

the

stack

after

stack

pressing

the

stack

.

..

to this.

T

0.00

Z

0.00

V

314.32

X

689.4

do

not

pressing

do

lift

m .)

...

Display

move

when a number

mum

when a new

or

rD3.

(How-

number

is

40

The Automatic Memory Stack

One-Number Functions and the Stack

One-number register are

unaffected

For

example

earlier exa contents

from

T

z

y

1--

X

The

one-number displayed that was in number

functions execute

only, and

when a one-number

, with

mple, pressing

...

this ...

0.00

l

0.00

I

314.32

689

~

Displ

X-regis

the

X -regi s

function

the

numb

ay

function

ter, and

ter.

.

contents of

ers

positioned

the

executes up

the answer

No

other

X

Two-Number Functions

and the Stack

Hewlettnumber instance, ifyou piece of

Pack

s in

paper

ard

the sta

'wa

and

calculator

ck

the

nted

to

add

then

write

s do

same

21

way you

34

and

underneath

34 21

upon

the

numb

the

Y -, Z-, and T -registers

function

[ill

T

1

f---

Z

lO.

Y

126.2~

register is

arithmetic

key

in

the stack

keys chang

to

this

.

0

.00

oo

314.32

~

J

on

only

writes over

by

would

21

you

wo uld

it, like this:

is

Displa

the

numb

affect

positionin g the

on

er

in

the

pressed.

as

es

the stac k

y

er

the

number

ed

by

pap

er. F

writ

e 34 on a

X-

in

the

in

the

a one-

or

and

then

you

would

Numbers are position

how

it

is

don

e.

(If

first

by

respond

pressing

to

a

those shown

add, like this:

34

+

21 55

ed the

same way

you clear the pr

~the

numb

in the example below

in the HP-25. Here

evio us

ers

numb

in the stack

's

er entries

will cor-

.)

The Automatic Memory Stack

41

Press 34

lED

21

Now so we

Press

[±J

The use

stack when the function key

this rule.

same before the

To

Display

34

is

keyed into X.

is

copied into Y.

34

21

writes

T

0.00

Z

0.00

Y

34.00

X

21.

over

34

can

I 34.

I

34.00

I 21.

and

21

are sitting vertically

add.

Display

The

155.

00

answe

simple, old-fashioned math notation helps

your

calculator. Both

in

the natural

Subtraction,

way

. In

operation

subtract

21

each

from

numbers

order

first; then the

is

pressed.

multiplication, and division work the

case,

the

data

must be

can be performed.

34:

34

-

21

Press Display 34

mum

21

B

To

1

1 21.

113.00

mUltiply

34

.

34.00

34

by 21:

34

is

keyed into X.

34 is copied into Y.

21

writes

over

The

answer.

JA

x

21

the 34

in

X.

in

the

stack as shown below,

1

Display

r.

exp

are

always positioned

operation

Ther

e are 110 e

in

the

proper

the 34

in

X.

lain how to

in

the

is

executed

xceptions

position

to

Press Display 34

mum

21

~

134.

134.00

121.

1

714.00

34 is keyed into X. 34

is

copied into Y.

21

writes

over

the

The

answer.

34

in

X.

42 The Automatic Memory Stack

To

divide 34 by

21:

34 21

Press

34

Imim

21

El

Display

34.

I 34.00 I 21. I

1.62

34

is

keyed into X.

34

is

copied into Y.

21

writes

The

answer.

over

the

34

Chain Arithmetic

You've

and perform calculations with them. In

needed to position the numbers

Imim

ments automatically. computing efficiency and ease that automatically store intermediate results. matically new number a calculation, any new digits you key ber. Also, the two-number operation.

+ 17 = ?

Note: of

already learned how to key numbers into the calculator

each

in

the

stack

key.

However

"lifts"

is

keyed in because

stack

If

you press mEl first, you will begin with

, the stack also performs many move-

These

automat

every calculated number

automatically

For

example, calculate

of

use, and it

it

knolVs

"drops

ic

movements add to its

is in

that

in

are a

" when you perform a

the stack registers, as the example below.

in

X.

case you first

manually using the

these movements

The

stack

auto-

the stack when a

after it

part

completes

of

a new num-

16

+ 30 +

zeros

in

11

all

Press Stack Contents

T 0.00

16 Z

Y

X

T

Z

Y

X

0.00

16.

0.00

16.00

16

is

keyed into the displayed

X-register.

16

is

copied into Y.

30

T

Z

Y

X

The Automatic Memory Stack 43

0.00

16.00

30

writes

30.

over the

16

in

X.

11

17

After

any

m

atica

tion s

of

the

calculation

lly lifts

are perfo

suc h chain

stack

regis

9.999999999 In addition to

s

tack autom

T

0.

Z

0

Y

0.

X

46.00

T

Z

Y

x

T 0.

z

y

X

T

Z

Y

X

T 0.00

z

y X

when a new

rmed

when

problems

ters excee

99

x

10

).

the autom

atically

drops

00

.00

00

0.00 00

0.

46.00

11.

00

0.00

0.

00

57.00

0.00

57.00

17.00

0.00

74.00

or

number

numb

the

is unlimited

ds

the

atic

durin g

16

and 30 are ad

The

answer

11

is

keyed X-register. is

automatically r

11

46 and

are add

The answe

17

is

keyed 57 is automatically into Y .

57 and 17 are add for

the final an

manipu

is

keyed

lation, the

er

operations are

unless a numb

range

of

the calc

stack

lift

after a ca

calculat

ions involving

ded

together.

, 46, is displ

into

the

displ

The

46

in

aise

ed

togeth

r, 57 , is

into

displayed

the

X-register.

entered

ed

together

swer.

sta

in. Because

pressed,

er

ulator

lculation, the

ayed.

aye

the stack

d.

er.

ck

auto-

ope

ra-

the

length

in

one

(up

both

d

.

of to

44

The

Automatic Memory

Stack

the X-and let' s

First 30 + II +

Press Stack Contents

16

mmiD

30 Z

mmiD

II

mmiD

17

do

the

pressB!3

17

Y-registers. problems

= ?

to

T

Z y

X

T

clear

differently

r---:-::

~

L 16.

I

z

Y

~

X

T

y X

T

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y

X

30.00

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t 30.00

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T

Z

30.00

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T

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30.00

y

11.00

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the

0.00

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16.00 I

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0.00

16.00

30.00

0.00

16.00

11.

16.00

11.00

16.00 l

17

~

happened

to

X-register.

16

X-register.

I

16 is

30 is

lifted up to

II register.

11 are respectively.

17

-l

in

the

see this

above

feature

Now,

is

keyed

copied

written

entered

is

keyed into the

is

copied

lifted up

is

written

example, but more

again solve

into

the

into

Y.

over

the

into

Y.

Z.

into Y.

to T and

over

the

clearly.

16

displayed

16

in

X.

16

is

displayed

16

and

30

Z

II

in

X.

+

The

T 16.00

Z 16.00

y

30.00

28.00

X

'----

,----

T

16.00

Z

16.00

y

16.00

58.00

X

1

T

16.00

Z

16.00

y

1

16.00

X

74.00

Automatic Memory

17

and

II

are

and

the

rest

of

drops.

16

drop also duplica 28

30 and

1

I

Now

be a

16 for s

tack

are and

dded.

and 58

the

rea

28

the

stack

16

and

final a

continue

dy

are

ted

to be a

58

Stack

added

th e s

tack

s to Z and

in

T . 30

dded

added

drops

are

ready

added

nswer

and

s to

drop

45

together

is

and

.

together again.

to

together

the

.

The same droppi

number Y, which

and

in T is

the

is

visible

This autom computing

m

ed

iate

results in

reentering

ng

action

duplicated

numb

ers

in Y

in

the

atic lift

and

power, since

long calculations

the

numbers.

in T and

X-register.

drop

you

Order of Execution

When

you

see a problem

5 x [

(3

you must

decide

Hewlett-Packard

starti

and

of

ave

tremendous

ng every

working

your

by

theses

power

h

-i.

whe

H P calculat

4) -(5

re to begin

applica

problem

outwa

versati

like this one:

-i.

tion s

lity

also

occurs

with

Z,

the

and

X combine to give

of

the stack

can

numb

give you

retain and position inter-

without

2) + (4 x 3)]

-i.

before you

engineers

at its

have

innermost

rd, you maximize

or.

Of

in

the

course, order of

with

El

, 0

and

G.

er

in

Z drops

the

answer

tremendou

the

necessity

(3 x .2

13),

ever press a key

determined

number

the

or

paren-

efficiency and

the

H P-25

execution.

The

to

,

s

of

.

th at

you

46

The Automatic Memory Stack

For

example, at the left side left-to-right

order,

right

is

lem ward. So, to

Press Display

3

mmm

4

El

5

mmm

2

El

B

4

mmm

3

3 I

mmm

.2

13

you

of

order.

however,

to begin with

solve

3.

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3.00

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0.75

5.

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==:

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o I 0.64

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o

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co

the

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uld

work

equation

All

problems

and

the bes t

the

innermost

the

problem

Intermediate

Intermediate Intermediate

(3 7 4) - (5 7 2).

Intermediate Intermediate

(374)

Intermediate

The The

the

problem

and simply working

cannot

order

above:

-

(5

first

number

final

answer.

above

be solved using left-to-

for solving

parentheses

answer

answer answer

7 2) + (4 x 3).

answer answer

answer

is

for

for for

for (4 x for

for

keyed

by beginning

through

any

and

(3

(572).

(3

prob-

work

74).

3)

x .213).

in.

it

out-

in

Constant Arithmetic

You

may

have

noticed

of a two-number

in

the

T-register

be used to insert a

that

operation

is

reproduced

oonstant

whenever

(not

into a problem.

the

because

there. This

stack

of

stack

mJ

drops

),

becaus

the

number

operation

e

can

The

Automatic

Memory

Stack

47

Example: A lation

typically culture of

each

Method:

registers Thereafter,

of day

and

1000,

for

Put

put

you

bacteriologist

increases

what

six

the

get

Press Display

1.15

Imim Imim

Imim

1000 0

0 0 0 0 0

When result

the the stack

Notice

causes time

rotates

number, but the

11.15

11000. 1

1150.00

11322.50 1

1520.88 174

1 1

2011.36

1 2313.06

you

press0the

(1150.00) is growth growth

drops, you

that

the

stack

the

stack.

9.01

factor factor

performing a two-number

number

contents

merely

will

consecutive growth

the

original

the

new

first

displayed

drops

into

is

duplicated

never

have

in

the

is

dropped.

of

the

shifts

tests a certain

by 15%

Growth

Growth Starting

Population Population

Population Population Population Population

each

be

the

bacteria

days?

factor

(1.15)

population

factor.

factor population.

time,

you

in

the

the Y -register.

from

to

reenter

T-register

However, the

stack

registers, does

the

numbers

day.

population

in

(1000) in whenever

now

after I st after

2nd

after

3rd

after

4th

after

5th

after

6th

calculate

X-register

the

T-register

it.

operation

to

be

strain

whose

lfhe

starts a sample

the

Y- , Z-,

the

X-register.

you

in

T.

day.

day. day. day. day.

1.15 x 1000.

and a new

Since a new

each

such

duplicated

mJ

key, since

not

are

rCll'ritc

already

that

at

the

press

time

popu-

and

copy copy

as 0

each

end

T-

0.

The

of of

the

it

any

in

Section 4

Function Keys

The

H P-25

p

art

plained. To

PROM-RUN

function

of a program.

LAST X

In

add

iti

on

to

int

ermediate resu

matic

register, the

the

value

formance register

Recovering from Mistakes

I L

AST

such numb

that

of a function.

into the

X I

makes

as

pressing

er.

use

switch

the

was

display

it

the

keys

In this

function

PRGM"

four stack

lts,

the

LAST

in

the

To

again,

easy

to

wrong

can

be used

section,

keys

RUN

registers

H P-25 also

X register. This regis

displayed X-r

place

pres

recover

function

manually

each

key

manually, ensure

is set to

that

cont

egister

the

contents of

s

c=J

from

key

or

is

individually ex-

RUN.

automatically

ains a

separate

before

.

keystroke

keying

keyed

ter

preserves

the

mistakes,

in

the

in

that

store

auto-

the

LAST

wrong

as

the

per-

X

Example:

by 3. 157.

Pre

ss

12

mum

3.1578

a I

LASH

o

2. 1

578

Divide

Display

1

12.00

3.8

1

I

3.16

I

12

1

15.

12 by 2. 157

2.

0

.00

56

after

Oops!

You Retrieves You're

The

correct

49

you have mis

made a

that

last

back

at

the beginning.

ans

wer.

taken

mistake

entry

ly divided

.

50 Function Keys

I n the

above

example,

of

the

stack

and

. . . from

this.

T 0.00 T 0.00

Z

~OO

y 0.00

X 3.80

This

made possible the

above.

when you

LAST

X registers

. . .

LAST X

1 3.16 1

pressed

correction

were

illustrated

..

Z

y

X 3.16 . 1

Recovering a Number

The

LAST

occurs

more

you do not Example:

Press

7.32

milE]

3.650112331

G

c:::::J

El

X register

than

have

Calculate

Display

17.32

13.6501123311

110.97 1

13.65 1

13.01 1

is

useful

once.

By

recovering a number

to key

that

number

7.32 + 3.650112331

3.650112331

Intermediate Recalls 3.650112331 to X-register.

The

in

calculations

into the

answer.

Prefix Clear

The

c:::::J

gold prefix

section

pressed,

then

press the

keystroke

Press Display

2

1iJ

(clear

prefix)

key

,

ma

5, Programming).

merely

correct

to that

press

of

another

key.

key

will

clear

, 1m ,

To

or

clear

mm

a prefix you

c:::::J as

For

example,

key during a calculation:

Oops!

You

of

the

sign but you key by mistake.

number

pressed

c:::::J, the

changed

to this.

answer.

a blueliJ prefix

(mm

the to

meant

.

~oo

3.80

in

the

where a number

using c:::::J ,

calculator

is

explained

have

mistakenly

change

a blue prefix

to

change

in

the display,

the blue prefix

contents

LAST

X

3.16

example

again.

key

1

, a

in

the

Clears The

sign, is

the blue prefix

correct

D I

PREFIX

am

I 1 2.00

1'--_2._00_ ----'

Number Alteration Keys

Besides altering they are

program

Absolute Value

Some of a number. display,

va

Press Display

To

Press Display

III

Integer Portion of a Number

To

D prefix

to display only the integers Press

123.456

D

When lost.

register.

mm

numbers. These

most

.

calculations

press

lu

e) key.

see the

absolute

~

extract

and

key

OEfJ

The

entire

there

are

three

useful

when

require the

To

obtain

the

III

For

1-3.

1 3.00

13.00 1 1+

Display

1

123.456

1123.00

is

prefix

example,

value

display the integer

followed by

pressed,

number, of

the fractional

keys

are ~ , I

performing

abso

absolute

key

followed by the

to calculate

1-31

of

+3:

31

portion

theCJ

of

the

Only

the integer

number

course,

(integer)

number

Function Keys

operation,

performed.

provided

FRAC

operations

lute value, value

of

the

absolute

ofa

key.

123.456:

remains

is

portion

.

portion

preserved

keystroke.

change

on

the H P-25 for

I and [[2J , and

as part

or

magnitude,

th e

number

~

(abso

value

of -3:

number, press

For

example

of

the

of

the

number

in

the

LAST

in

of

lut

51

a

the

e

the

,

is X

Fractional Portion of a

To

place only the fractional portion

pl

aye

d X-register, press the

Number

of a number

III

prefix key followed by the

into the dis-

52

Function Keys

I FRAC I (fraction) key.

tion

of

123.456 used abo!:e:

Press Display

123.456

m I FRAC I 0.46

When

m

~

is

pres

lost.

The

entire

number, of

register

Reciprocals

To register, then

Press Display 25

You calculation calculate

Press Display 3

6

[±J

m

Square Roots

To X-regi s of 16:

Press Display

16

To Press Display

D I

.

calculate

rocalof25:

m

00

can

m

oo

m

oo

calculate

ter

D

[ill

find the

ff

I

the reciprocal

press

0

1L...:..:

--=-04-'---_--'

.

also

calculate

without

0.

33

0.17

0.50

I 2.00

the

square

, press D

"---.:4.-'--

00=---

square

LI

2

---'-.0-'--'0'----_---"

root

For

sed,

course,

moo.

the reciprocal

reentering

root

[ill

.

For

_--'

of

the result:

example,

Only number here

the

of a number

For

113

Reciprocalof3 Reciprocalof6

Sum

Reciprocal

to

the fractional

is di s

to

normal

integer

is

preserved

example,

of

the

number.

+ 1/6

of

reciproc

of

of a number

example,

see

the fractional por-

portion

played, rounded

FI

X 2 displa

portion

of

the

in the

in

the displaye

to

calculate

a value

sum.

to find the

in a previou

For example, to

. .

als.

in

the displayed

y.

number

LAST

the recip-

squa

re

of

d X-

the

roo

is

X

s

t

Squaring

To

square a number

~.

For

example,

Press Display

45

III

~

I

2025.00

To

find the

Press

square

of

Display

I

4100625.00

in

the

displayed X-register, press III

to find the

the result:

I

square

Function Keys

of

45:

53

Using

The

a fixed

you need it

Press Display

3

1lI

Example: tion pizza

equal

have

.

pizza?

Press Display

211mim

2

1lI

III 0 1 3.

o

Pressi ng

stack

Pi

value

7T

constant

in

0 0

,-I

Trencherman

of

the

Guinness Book

ever

baked

to

the

task,

to

devour

1

El

1

0 1

~I

III 0

to lift.

accurate

in

a calculation.

_9._

42

_ _

had a di

how

in

21.00

10.50

110.25 14

~3=:4'='

6.~3

causes

to

10

places (3.141592654) is

the HP-25.

~

many s

order

==6==;

Merely

For

example

Buck Mulligan looks into a

of

Records

ame

ter

of

21

quare

consume

Square

feet

in

to

the results

provided

press III 0

, to

calculate

and finds

feet.

If his

of

pizza would Mulligan

all

of

the

of pizza

the automatic

whenever

recent

that

the largest

appetite

world's

.

as

37T:

edi-

were

large st

memory

54

Function

Keys

Percentages

The

[JJ

key

is a

compute

1.

2.

3.

4.

For

$1500:

Press Display

1500

6.5

III

6.5%

In

ca

lcul

reg

When

percentages. To

Key

in

PresslmimJ.

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in

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III

examp

le,

ImimJ

[JJ

of

$1500 is $97.50 .

the

above

ated

you

answer

pressed

ister, and

the

base

the

number

[JJ

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to calculate a sales

1

1500

.00

;:::

16=.5= =

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19~7.~50~

example,

the

base

two-numb

number.

representing

=!

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when

writes

over

number

III

[JJ

,

the

er

find

Base Percent

The

answer.

the

is

preserved

stack

function

the

tax

number.

III

contents

that

percentage

percent

of

6.5 %

rate

.

[JJ

keys

percentage rate

in

allows

of a number

rate

.

on a purchase

are

pressed, the

the Y-r

were

in

egister.

changed ...

you

the

to

;

of

X-

. . .

from

T

0.00

Z

0.00

Y

1500.00

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6.5

Sinc e th e

of

tax

is in

s

imply

Press

this

...

purchase pri

the

adding:

Display

11597.50

X-regis

ce

is

now

ter, the

Total

. . . to this .

T

0.00

Z

0.00

Y

1500.00

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97.50

in

the Y-r

total

amount

of

price

egister

can

and sales

and

the amount

be

obtained

tax

combined.

by

Storage Registers

In

addition to

provided by

HP-25 also has eig affected by a

ll

ow

you to calculations ofa

program.

automatic storage

the

four-register

ht

operations

set

, and

addressable

aside

they

within numbers

can

of

interm

automa

storage

the

stack.

as

constants

be used ei

Fu~c~o~

ediate

tic

memory

registers

These

or for use

ther

manually

Keys 55

results

stack

that

storage

or

that

is

, the

are un-

registers

in later

as part

Automatic Memory

Stack

I

LAST

X II

~

I

D;,pi,y

The

addresses

keys@]through[IJ,

of

the

storage registers

as

shown

above.

Storing and Recalling Data

To

store

a value

followed by a

ter

address where

store

Avogadro

register R

Pre

6.02

Em] 2

When a number register , so 6.

To display , of

the register

:

2

ss

m:1

23

copy a number

press

appeari

ng

number

key

(@]

the value

's

number

Display

I 6.02 23 I

I 6.0200000 23 I

is

stored, it

02 x 10

23

also remains

from

one

the

liD

(recall) key

address.

in

the display, press m

through[IJ)

is

to be

(approximately 6.02 X 10

The register R

is

merely

of

the

Storage Registers

I I Ro I I R,

I I R2 I I R,

I I R, I I R,

I I R,

are

indi

cated

specifying the regis-

stored.

number

in

the

storage

followed

For

is

now

•

2

copi

ed into the storage

displ

ayed

registers into the

by the

by

number

(store)

examp

le, to

2:3

stored

X-register.

number

)

key

in

56

Function Keys

For

example,

Press Display

to recall

10.00

I 6.0200000 23

Recalling a

keystroke When

into

can

recall a without register until you

clear Example:

14.4, approximately of

the

number

was

you recall a

the

display,

number

altering

as a 10-digit

you

overwrite

the

Three

and

55.0 gallons,

tanks

?

mmiD

number,

and

it-the

storage

tanks

equal

causes

it

from a

number

it by

registers.

to 3.785 liters,

Avogadro's

the

stack

,liD

or m (more

it

is

also

remains

storage

number

with a two-digit

storing

have

capacities

respectively.

to lift

copied

in

register

will

another

what

number:

unless

abo

from

the

storage

any

remain

number

in

U.S.

If

one

is

the

preceding

ut m later).

storage

number

exponent

capacity

register

register.

of

in

the

storage

there,

or

units

of

U.S. gallon

of

You

times

of

10

until

2.0, is

each

Method: registers

Press Display

Place

and

the

bring it

conversion

out

as

required

constant

.

liD 10.00 I

D

0KJ

3 1 0.

3.785

EmJo

20

14.4

_0

0 154.504 1

55

go

0 1 208.175 I

0KJ

2 1208.18 1 Display mode reset.

D

Clearing Storage Registers

To

clear

the

quantity

the

number

To

clear

data affecting This

turning

data

places

the

000

,13.785 1

1 7.570 I

number zero

key

zero

calculator 0 FF

from a single

in

the

register

(@]through[IJ)

from all manual

in

other

portions

in

all eight

1

Display Constant Capacity Capacity Capacity

storage

by pressing@]

of

the

storage

of

the

of

the

storage

also

clears

in

one

mode

placed

of

I st

of

2nd

of

3rd

register, simply

EmJ

register registers

address.

at

calculator,

registers.

all registers.

of

the

set.

in

register

tank

in

tank

in

tank

in

followed by

once,

pressD~

Of

storage

Ro·

liters.

store

without

·

course,

Storage Register Arithmetic

Arithmetic

ster

followed in

by

is

performed

pressing

turn

upon the conte

llmJ

followed by the

by

the

register address.

Functlo~

nts

of

th e storage regis-

arithmetic

For

example:

Keys

57

function key

Press

llmJ

I:±ll

When

storage

answer

contents

rema

Example:

cannery of25 pays per

is

in

unchanged

tons him $55

ton,

and

of

for

, 27

deducts 2% blight

on

the

farmer's

Keep

to

add

is

Method:

stack

Press

25

IDa

271:±l

191:±l231:±l

550

Result

Number tents

of

R,:

(r

, + x --'> R

Number contents placed into R

Contents in

display

:

R

(r

-7

4

regis

the

displayed

ter

into

written

.

During

three

he

of

ton per

ships

the

harvest

days.

s,

19

ton.

price

loads

tomatoes, and

tot

al

net

total a

tonn

ages

Display

,--,I

9

:....:

4=.0"'-0

1

5170.00

in displ

of

storage

:

2

ayed

register

,

).

ayed

(r

2

storage

in displayed

of

storage

:J:

[ (r

of

storage

ed

X-register, and

x

--'>

R,),

arithmetic

the

selected

X-register

, a

On tons, On

farmer

Monday

and Wednesday of26

on

Monday

3%

of

income

?

mount

in a

and

calculate

_----'

X-register

added

R" and SUm

X-register subtracted

register R

- x

--'>

Rz).

,

2

X-register

register

)

x --'> R

3

register

,

R

and

3

].

3

R4 divided by

quotient

operations

storage

and

are register

the

rest

trucks tomatoes

and

Tuesday

23

tons,

for

which

the

tons

the

storage

Total Tuesday's

Gross

and

price rises to $57.50

and

28

ton

s.

and

Tue

price

sday

on

Wednesday,

register

amounts

of

Monday's

of

tonn

amount

Tuesday.

to con-

placed into

from

and difference

mUltiplied by

the

product

number

placed into

performed,

, while

of

the

stack

to

the the

the

he hauls loads

the

cannery

If

the

cannery

because

what

while using

the

loss .

and

age.

for

Monday

of

58 Function Keys

Gross

as

I 5170.00

placed

register R

21]lYJ

103.40

Deductions Tuesday

Deductions

in

storage register R

total Wednesday Gross

amount

Wednesday's

26miimJ28El

57.500

EmJ

El5

103.40

I

54.00

I 3105.00

I

3105

.00

added to total register R

I

93.15

I

93.15

Deduction

Wednesday tracted

from total

register R

The

8078.45

farmer

from his

tomatoes. (You could also work this problem using the illustrates how storage register

ar

ithmetic

Storage Register Overflow

If

the

magnitude

exceeds

shows

~

overflowed.

For

example

to

calcu

late the register overflows and the display result

of

storage register overflow:

Press Display

050

mO

7.5050

EmJ00

To

clear a storage register overflow displ

ofa

number

9.999999999 x

(a

ve/flow)

,

if

you use storage register arithmetic to

the

product

1.

0000000

in

any

99

,

10

the HP-25 display immediately

to indicate

of

I x

10

50 I 50 I

of

the eight storage registers

that

50

and 7.5 x

1 x regi

7.5

OF

50 I

When you mUltiplied using storage register arithmetic , register

a storage register has

shows

50

10 ster

in

storage

.

5

for

Monday

.

subtracted

's tonnage.

for Wednesday.

gross

amount

in

storage

.

5

for

Wednesday.

deduction

in

.

5

's total

net

stack

alone,

works.)

50

10

in

register R

[QIJ. To

pl

aced

into storage

Ro.

Ro overflowed.

ay,

merely press

and

from

.

5

sub-

storage

income

but

attempt

see

o

the

it

,

Trigonometric Functions

Your

HP-25 provides you with six

also

calculates

converts

it

seconds

Trigonometric Modes

When

the HP-25

specified press

the

(grads).

press

the IlIshift key followed by

Note:

360

Functions

The

six trigonometric functions

D

~

(sine)

III

~

(arc sine)

D

~

(cosine)

III

~

(arc cosine)

D

~

(tangent)

1lI

~

(arc tangent)

Each

trigonometric function radians, functions, so to use

function key s.

Example 1: Find

Press Display 35

D

~

Example 2: Find the arc sine

Press .964

1lI

~

1lI

~

angles

in

between

decimal

.

is

first

turned ON,

in

decimal

degrees.

III shift key followed by

To

switch back to the

degrees

or

grads.

!35.

! 0.82

Display

! 0.964

! 0.96

!82.87

=

27T

radians

assumes

Trigonometric

them

you key

the

cosine

of 35°.

in

degrees,

degrees

To

decimal

the~(degrees)

= 400

provided

in

Calculator decimal

The answer.

grads

Grads Grads.

Function Keys

trigonometric

radians,

and

degrees

it "wakes

set

radians

either

~

(radial1s)

degrees

grads

by the

angles

in

decimal degrees ,

functions are

the

number,

"wa

degrees

of

.964.

mode

is

59

functions.

or

grads; and

, minutes,

up" with angles

or

grads mode,

or

~

mode again,

key.

calculator

are:

one-number

then

press

the

kes

up"

in

mode .

set.

It

60

Function Keys

Hours, Minutes, Seconds

The

I +H.MS 1 (to hours, minutes, seconds)

hours

to

the

format

of

hours digits for Forexample,

Press Display

12.56

D~4

D I +H.MS I

Conversely, hours,

convert hours:

Press Display

seconds, you should specify

to

convert

1

12.56

112.

5600

1

12.3336

the

EEl

minutes,

12

seconds

hours, 33

112.5600

Hours to hours, minutes, seconds

decimal The

minutes, For

Press

137.4512

D

The

the H P-25

hours

EEl

and 1 +H.MS I

seconds

example

EE]

conversion

operate

.

to decimal

, to

change

Display

1137.4512

1137.7533

is

important

on angles

keys

degrees, minutes, sec

of

metric functions you

must

first

Example:

of

Tristan

Penelope, course isolated

island

Lovesick

da lives

of

true

inhabited spot

of

St.

an angle given in

convert

sailor

Cunha

on

the

love ,

Helena

, minutes

12.56 hours to

(to decimal hours) key

into decimal

minutes, 36

also

permit

degrees, and

137

°45'

12"

because

in

onds

. In

order

the angle to decimal

Osc

(37°03' S, 12°18'W),

however,

(15°

ar

nearest

in

the

world.

55'S, 5°43'W)

key

converts

and

seconds. To

FIX

4 display format.

hours,

minutes, seconds:

Decimal Sets display format.

This

minutes ,

Decimal

conversion

Decimal

de

Odysseus

island.

Tristan

hours.

is

read

as

12

36

seconds

is

used to

hours.

seconds

to decimal degrees:

trigonometric

back

hours.

you

to change

vice vers a .

degrees.

For

is

accurate

cimal de grees,

to

calculate

degrees, minutes,

degrees

dwells

and

his

Unfortunately

da

Cunha

If

Penelope

, use the following

decimal

see

the

hours,

33

.

change

example,

into decimal

functions in

but

any trigono-

.

on

sweetheart,

is

lives

to

to 10-

degrees,

not

in

seconds,

the island

for

the

most

on

the

5

formula to calculate the great circle distance

must sail

Solution:

decimal degrees as you key them

circle distance from

land is:

Press

5.43 11 @ 5.72

12.

O

15.55 1I@ 1lmJ1

o

37.0311 @ 1lmJ01

O

o

1m

_ 1 0

in

order

to

court

her.

Distance

cos

(LAT,)

Where

LAT

LATd and

Convert all

Distance

cos (37° 03') cos (15°55') cos (5°43'W -12° 18'W) ] x

18

II@El

~

00

~ ~

= COS - I [ sin

cos

(LAT

s and

LN

source (Tristan

LNG

d

degrees, minutes, seconds

Tristan

=

COS-I

Display

0.

00

0.00

1;=

-~6.~58~===;

1 0.

99

F=

I

=15

==.9~2==:

1 0.96

~

=====:

i=1

=0=.9=6

==~

37.05

1 0.

80

1

i==0.~76~~

I 0.

60

:=1

=0.=2=7 ====i

(LAT

) cos

(LNG

d

G

= latitude and longitude

s

da

= latitude and longitude

destination.

in. The

da

Cunha

[ s

in

(37°03') sin

Display mode (Assumes from previous example.)

Sets decimal degree mode for trigonometric functions.

,) sin

(LAT

-

LNG

d

Cunha).

equation for the great

to the nearest inhabited

(15

°55') +

no results remain

that

)

d ) ] x 60.

s

of

entr

is

set.

Odysseus

+

of

the

ies into

60

o

El

II

~

60

0 1 1315.41

i=1

=0.=1=7

1

~I

~2~1~

==

~

0.93

.9

=:'

2==:::;

Distance Odysseus Penelope.

in

nautical miles that

must sa

il

to visit

62 Function Keys

Polar/Rectangular Coordinate Conversion

Two

function s are provided for polar/rectangular conversion. To senting rectangul

(J

coordi

Magnitude r then in

the Y-register.

Conversely, to senting polar r, respectively), press

convert

nates (magnitude and angle, respectively), press

convert

(J

values

in

ar

x, y

coordinates

appears

values

, respectively) to rectangular

the X-and Y-registers, (repre-

, respectively) to polar r,

in

the X-register

in

the X-and Y-registers (repre-

0.

and

angle

coordinates

coordinate

m~.

is

placed

(x , y

Example

with the angle

Press

m

31mim4

m

1:

~

m'J

Co

nvert

expressed

y

Display

10.

14.

1

5.00

10:

rectangular

in

radian s.

e

00

I

64

coordinates

(4,3) to polar form

(4,3)

x

Specifies radians mode. (Assumes from previous

Rectangular placed

Magnitude r. Angle

no results remain

exa

mple

coordinates

in X-and Y -registers.

(J

in

radian s.

.)

Function Keys

63

Example

coordinates

2:

Convert

.

(X,y)

polar

r=8

coordinates

y

(S, 120°) to

rectangular

x

Press Display

m

~

120mimJS

a

~

EiD

1 0.00

1

8.

1-4.

00

1 6.93 1

Specifies (Assumes from previous Polar placed respectively.

x-coordinate y-coordinate.

degrees

no results remain

example

coordinates

in Y -

and

.

mode

.)

(!

and

X-registers

Logarithmic and Exponential Functions

Logarithms

The

H P-25

as

their

well

a

lli!J

m

~

a

[IQ9J

m

~

Example

tude

of

S.25

greater

than

magnitude

computes

inverse

is

loge X-register is

antilog,. (na

power

the

of

value is

loglo

in

the

is

antilog

of

the

1:

The

on the

of

the latter

RI =

both

functions

(natural

X-register

value

the

log) .

to ba se e (2.7IS

tur

of

the value

e,

pres

s I m

(common

lo

in

the

1906

San Francis

Richter

Nic

aragua

on

R2

- log

natural

al antilog). It raises e (2.7IS

log).

to ba

the

M;

and

(antilogarithms) :

It

take

~

It

se

antilog). It raises

X-register.

Scale

quake

Richter

M

.,

= S.25 - (log

common

s the log

...

) .

in

X-register.

.)

compute

10.

co earthquake

is estimated

of

1972.

Scale?

of

the value

(To

s the log

10

, with a magni-

to be

What

The

105

-1-)

loga

display the

of

to

would

equation

rithms

...

the

105

.

r

in

the

) to

value

power

times

be

the

is

,

as

64

Function Keys

Solution: Press Display

25miiE]

8. I 05a

[1Og]

~18~.2~5

~12~.0~

2

=~

B 16.23 Rating

Example

ba

rometer sure ca tes

pre ss ure and altitude is a function knows

Where

Solution: Press

301m1m

9.48

a

25000

o

Quarmorte (29,028

Raising Numbers to Powers

a 0 permits you to raise a positive

or 2

x 2 x 2 x 2 x 2 x 2 x 2 x 2).

Press 2miiE]9

Now Press 8miiE]

1.2567 In

extract equivalent to 5'/.')

2:

Ace

explorer

as

that

an

is Jaso n

is

ft).

[ZJ

rmJ

a 0

roots. F

an altimeter.

of

mercury) he climbs until the

of

mercury

approximation

Quarmorte

Display

130.00 19

13.

11.

16

125000.

129012.

probably

with or

..

near

Display

1512.00

Display

18.00

10.07

oo

ex ample, find the

(30 inches

9.4 inches

Altitude (feet) = 25,000

~

a decimal) to any power.

find 8 - 1. 25(;7.

conjunction

Jason

Quarmorte

After

mea

suring the

. Although

is given by the formula:

In----

Pressure

?

19

the summit

For

,a

[ZJ

the

of

many

30 30

Altitude

number

example, calculate

provide

cube

on

Richter

is using an

sea

barometer

exact

factors, Quarmorte

=

25

000

' 9.4

in feet.

of

Mount

(either

s a simple

root

sca

ordinary

level pres-

relationship

tn--

Everest

an integer

29 (i.e., 2 x

way

of

5 (This

le.

indi-

of

to

is

Function Keys 65

Press

Example: 25

,500 feet with a calibrated airspeed (CAS)

is

the flight mach number

if the following formula

M=

Method:

is

at the innermost set

quantity Press Display

350mmiD

iii

[£]

.

201

3.5 0 0 1

I

mmiD

ram

255000

5.2656

01EJ

.286 0

An aircra

The

t

6!~~5

661.5 B

EJ

6.875

6

mmiD

EJ I 0.82 I

Eml

0 0

1EJ

500~

Display

I

5.00

I

0.33

:=

1 =

1.=71

======i

ft

pilot reads a pressure altitude (PA L

speed

M =

---:-----,,---,-

speed

is

applicable?

most efficient place to begin work on this problem

of

brackets. So begin by solving for the

of

aircraft

of

sound

I

1

j 2 and proceed outward from there .

:=

1

0=.5

o=3===

I 0.28 I

11.06 I

I 0.21 I

'--"'=-=-

--

_I

6.875

I 6.

8750000

1:=

2~.~76~=====i1

rl-

1.5-8------~

I 0.14 I

1

0.84

-

00

-06

~1

---'

I

1

I Ma

Reciprocalof3.

Cube

root

of

5.

of

350

knots. What

Squar

~

of

quantIty .

Contents

of

brackets are

the stack.

Contents

et

s the stack.

bracketed

ofleft-hand

in

of

chnumberoftheflight.

right-hand

brackets are

T)of

set

in

66 Function Keys In

working through

levels

of

six of

the Hewlett-

one

step

see

every

tionconfidentofyourfin~answer.

parentheses

at a time , you

intermediate result, and you emerge from

complex

Packard

don't

above

equations

, you really

, like the

appreciate

one

containing

the value

logic system. Because you calculate

get

"lost

" within the problem.

the

You

calcula-

Statistical Functions

Summations

Pressing the m key automatically gives you several different

sums

and

once.

In

order statistics lator

problems,

into storage registers

information is isters is when the

lations using the

products

registers When

each

of

data

you key a

of

the

following

The

number

contents

to the

The

square

register

The

number that you keyed into the X-register

the

contents

by storage register R The

number contents The

number 1 is

number

not

does

Thus,

each

press

multiplications. the applicable storage registers

Register Data

Displayed X n

of

the

values

in

the X- and Y- registers at

to make these values accessible for sophisticated

they

are automatically placed by the calcu-

•

The

only time

7

in

the storage reg-

that

automatically

R3

through R

accumulated

m key is used. Before you begin any calcu-

m key, you should first

by pressing

number

operations

that

of

added

the

to the

is

of

in

the

of

storage register R

added

in

R,;

is

then written into the display

lift).

of

the

The

contents

n

D.

into the display and

is

you

keyed

storage register R

number

contents

the Y-register,

.

5

Y-register

to storage register R

m key updates these

of

are

Number Number

of of

performed: into the X-register is added

that

of

•

4

the displayed X-register

as follows:

entries.

entries .

clear

the storage

press

the

m key,

•

7

you keyed into the X-

storage register

and

the

product

the

stack

is

R,;.

is

multiplied

added

to the

and the total

,

3

(The

stack

summations

and and

to

LY

R5

R6

R7

In

addition , the y-value

key

is fore m To

see

call the the m key, number

played. Example:

and

y listed

LXY Lx2 LX

retained in

was

pressed

any

of

the

contents

recalling storage register

simply

The

writes

stack

Find

LX, Lx2, LY,

below.

Summation Summation Summation Summation

present

the

Y-register, while the x-value

is

retained

summations

of

the

desired

of

of of

before

in

at

any time,

storage

y values.

products

X2

values .

x values.

the last

the

register.

contents

over

the

does

number

not lift .)

and

LXY

of

for the

Function Keys 67

ofx

and y values.

press

of

the m

LAST

you

entries

present

X register.

have

(I

n

the

or

keying in a

(11)

paired

be-

only to re-

case

that

is dis-

values

ofx

of

Press

a

7

mmiD

5m 5

I:mim

3m

9

mmiD

8m

1317 1316

1315

1314 1313

~

Display

t 0.00

17.00 1

1.00

1

5.00

12.00

19.

00

13.00

116.00 1

98.00

1

122.00

121.

00

13.00

Mean

The

mean (arithmetic average)

them

key

is

avail able by using the

I I I

I

I I I I

Ensures are

that

cleared (Assumes from

Second pa

All

Sum Sum

register

Sum

is

ir

the data

ofx

values from regi ster R

of

squares

R,

;.

of

products of x a

from register Sum

ofy

values from register Ro!.

Number

of

data

of

entered

[KJ

all

storage

to

zero

no results

initially.

registers

remain

example.)

summed:

is summed :

is

11

summed;

of

x value s from

=

11

nd

y values

I.

= 2.

=

3.

7

Ro.

entries (n = 3).

and

summed

using

(meal1)key. When you

•

68

<""unction

Ke\'~

pressD data

The

cab above.

in

Example: A

United States to have the following ages:

To

persons:

Press Display

62 68

71 D

rn

, the mean

in

storage registers R3

easiest way to acc umulate the required d

le registers

However,

storage registers R3

survey

62

84

find the average (mean) age

Ell

,

84

Ell

,

Ell

,

60

Ell

,

73

Ell

rn

of

the values

(n)

-

x = - L.J

is

through the use the required data may also be stored directly

(n)

and R7

found ten

47

58

68 60

47

Ell

,

58

Ell

62

Ell ,

59

Ell

of x is calculat

and R7(lx)

n

I"

n i = 1

~-'=

of

0.00

Xi

of

(lx)

the wea lthi

of

'----'

, '

1,-

1-0.-00----,1

1 64.40 1 A verage (mean) age

Standard Deviation

The

standard deviation (a measure

mean)

is

calculated usi

and

the@](standard

in

registers R3lll),

deviation according to the formula:

ng

deviation)

Ru

(lx

data

2

),

and

of

in

the

applicab

key. Pressing @]uses the

R7

(lx)

ed

using the

and the formula:

ata

in

the appli-

the

Ell

key as described

, if desired.

est

persons

62

59

71

this sample

1 Storage registers

and X-register cleared to zero.

N umber

in yea rs.

dispersion around the

le storage registers

to calculate the standard

73

of

entries .

in

wealthy

data

the

For

examp

problem :

S

x L.Jx -

le, to

=

J"

obta

in

the

2

n-I

samp

(lX)2

--

n

le deviation

in

the above

Press

If

the

10

wealthiest

population

sample

deviation

standard

Display

110.10

persons

persons,

rather

(s')

is

used

the

data

than

as a

deviation

illustrated

Standard

in

the

sample

would

sample. The

(s)

and

by

the

following

Function Keys

deviation.

were

have

to

relationship

the

population

equation:

actually

be

considered

69

the

10

as a

between

standard

~

=sv~-n--

accumulated

the m key,

deviation,

standard

example,

this way:

Since

11

is

data

are

accumulated

vert

the

calculated,

For

example,

are

still

intact

population

automatically

sample

standard

to

population

if

the

from

standard

s'

by

accumulations

the

deviation

Press Display

o

@]

liD 3 10.00

1

EJ

1i!D3@ 1 0.90

o

~

10.10

9.00

0 1 9.58

Sample Recalls Calculates Divides

Population

standard

11.

11-1

Deleting and Correcting Data

If

you

key

in

an

lD3

and

If

one

pressed

correct

1.

Key

2.

Press

3.

Key x, y reentered

Press

4.

key

in

of

the

values

the m key

the

summations

the

0 IE] to

in

the

data

m.

incorrect

the

incorrect

correct

pair

.)

correct

is

changed,

that

data

delete

is

incorrect,

value

and

value.

or

if

one

of

the

by using the

pair

into

the

incorrect

values

for x and

both

have

you

values

in

register

it

is a simple

which

in registers

you

11-1

.

by 11.

standard

not

discover

lEl

key

the X-and Y-registers

data.

y.

values

matter

has

R3

can

deviation

pressed

after

is

in

error, you

as follows:

(If

one

must

be

R3

when

already

through

calculate

(s).

m ,

you

value

deleted

to

been

(s')

press

ha

of

the

con-

R7

the

.

ve

can

.

an

and

70

Funclon

The

correct

obtainable

For

example, as given persons futures.

sample

in the

Press

62

D

~

21

Ell

The

new

present standard

K-

values

by

pressing

suppose

above

were because To

data

in

deviation :

of

account

by a 21-year old Display

62.

9.00

21.

10.00

has

the

storage

for

mean

and

stand

[Xl

and

~

the 62-year old

to lose his position as

a series

been

for

the

calculated

registers.

of

ill-advised

change

rock

Data

to be repla Number The

new

Number

into To

ard

.

member

one

investments

in

data

musician:

of

entries

dat

a.

of

entries

each

see the

deviation

of

if he were replac ed

ced

(n)

of

the

are n

of

the

wealthiest

in

.

is

now nine.

is

ten ag ain .

summations

new

mean

sampl

coc

and

ow

oa

e

Press

D@

DO

Display

60.30

17.09

The The

Vector Summations

The

Ell

key

can

be

used

to sum

and

Y -registers.

subtraction

and

the

Ell

Example: In his

pilot

Apeneck heading being buffeted by a What

fish?

Method:

of

are

the in gular

of

is

the actual

The

the

instrument

converted

Ell

and

storage

coordinates

You

using

rectangular

and ~ keys

converted

Sweeney

0450 from his

[[]

registers R4

headwind

ground

course

vector

to

rectangular

keys. Their

are

can

even

.

reads

instruments. The

speed

and

ground

and

sum

O:y)

and

then

converted

new

average

new

standard

any

quantities

perform

to polar

Swordfish aircraft,

an

air

of

40 knots from a bearing

and

speed

the

wind

coordinates

is recalled by recalling

R7

(Ix),

back

(mean) age .

deviation .

that

vector

coordinate

speed

of

Swordfish is also

course

are

equal

vector.

and

to

polar

150

of

summed

the

are

in

addition

conversion

grizzled

knots

of 025°

the Sword-

to

the sum

The

vecto

the

new

rect

coordinate

the

and

bush

and a

using

valu

x-

.

rs

es

an-

s

Function Keys

71

to give the

Press Display

a

~

m

~

45miim

150

a

~

fm

25

miim

40

a

~

a

lE]

-

vector

course

~ ~A'

__ ~ _____

I 0.00

145.00

I 150.

106.07

1.00

I 25.00 I 40. I

36.25

I 0.00

4

7

89

.16

69.81

-

m

~

aD

113.24

51.

94

of

the

actual ground speed

150 knots

0

45

j

o

o o

'L

--~

Clears storage registers. assumes no results remain from previous examples.) Sets degrees mode. ()

for the Swordfish instrument vector. r for the Swordfish instrument vector.

Converted

nates. Instrument ulated

()

for wind vector. r for wind vector. Converted coordinates. Coordinates subtracted Swordfish's

Recalls sum

register R4.

Recalls sum

register R

lifted to Y -register.)

Actual ground Swordfish

Course degrees.

and

~: ~

40 knots

~

Actual ground speed

~

_____

to rectangular coordi-

coordinates

in

storage registers

to rectangular

for wind

from coordinates for

instrument vector. ofy-coordinates

of

•

(Sum

7

in

knots.

of

the Swordfish in

vector

x-coordinates from

of

y-coordinates

speed

of

course

90°

(Display

accum-

R4

and R

from

the

.

•

7

- / t .

Section 5

Programming

As we briefly explained

is

as simple as pressing the keys you would manually press

ming to solve programming featuring:

Together

to tackle complex problems with unabashed confidence.

What

A program strokes execute the program as often as you like with less

error. one manually . HP-25 calculator programming .

your

problem. But

is

simple to understand and use, it

An

obvious

• 49

usable

•

The

• Decision-making capability for sophisticated routines.

• Several editing operations to facilitate corrections.

The

you would have obtained by pressing

steps

ability to combine several keystrokes into

these

features provide you with the tools necessary

is

a Program?

is

nothing more th an a

that

is

remembered by the calculator. You answer No

prior programming experience

in

the introduction, calculator program-

even

though HP-25 calculator

programming language .

of

program memory.

sequence

displayed

at

the end

of

execution the

is

very powerful,

each

of

manual key-

can

chance

is

necessary

the same

at

keys one

step.

then

a time

for

Why Write Programs?

Programs are written to save you time on repetitive calculations. Once

you have written the keystroke procedure for solving a particular problem and recorded it no longer make up the procedure.

problem for you. And bec ause you can easily dure answer or

not you have forms the drudgery, leaving work.

devote

in

your program, you have more confidence

since you don ' t have to worry

attention to the individual

You

pressed

an incorrect key.

in

the calculator , you need

can let the calculator solve each

each

your

mind free for more creative

keystrokes

check

time

about

The

calculator

the proce-

in

your

whether

that

final

per-

73

of

74

Programming

Three Modes of Operation

There

are

three

ways

to use

your

HP-25 calculator:

UN

I. Manual R

2.

PROM

3.

Automatic

mode

RUN

Manual RUN Mode

The

functions and

first four at These

sections

a time with the

functions

enable you to calculate

operations

of

this

PROM-RUN

combined

mode

handbook

any

PRGM" PRGM'-RUN

PRGM"

you have learned

are performed manually

switch

with the automatic memory stack

problem with

set

RUN

to

ease.

RUN

about

P.oM"

in

the

one

RUN.

PRGM

In have in

execution.

be recorded set to

be recorded

PROM

learned

a part

PRO

Mode

(program)

about

of

the

All

for

M

are

mode the functions and

are not

calculator

operations

later

execution

PRGM

'-RUN

:

mI

1m

a I

These

three

and record

your

Automatic RUN Mode

The

HP-25

can

of

operations

PRGM"

memory. the recorded

RUN

mode

key and the more quickly

with the

RUN

if they have previously been recorded

Instead

operations

when

entire

than

work

programs .

also be used to automatically

PROM-RUN

of

your

having to press

are

you

press[E[]

list

of

recorded

you could have

executed,

called

on

the

keyboard

with the

•

The

three

PRGM

in

PROM

executed

(rul1/

operations

but

instead are

program

memory

except

PROM-RUN

operations

I

that

mode to help you write

execute

switch set to

each

key manually,

sequentially

stop).

executed

in

You press only

is

executed

them yourself.

you

recorded

for

later

three

can

switch

cannot

a list

RUN

in

program

automatic

one

much

Programming 75

Introductory Program

The

area ofa sphere program you wrote, recorded, and executed

in

the introduction showed you that the sequence

is

used to solve a problem manually a program . exp

lain the informa tion displayed in

Now

let's return

the same s

our

attention to that program to

PRGM

equence

mode .

of

keystrokes

used

in

First, set the so th

at executio of

previous programs.

This tells you that yo u are at the beginning

Step

00 used to are

recorded

PRGM-RUN

the sequence

n. Second, press D I PRGM I to clear the calcul

contains an

record

in

Stack

automa

your

program key s

steps

01

of

switch to

keys trokes w

The

display wi

I 00

tic stop instruction and cannot be

through 49. (See figure below.)

Storage

ill

ll

trokes

show:

Ro R, R,

I

LASTX

I

W

R3 R. Rs R6 R7

PRGM

be re

of

. Program

PRGM'-RUN

corded

program memory.

keystrokes

Program

r---....

Memory

Step Step Step

Step Step Step Step

for later

ator

00 01 02

..........

46 47 48 49

76 Programming

As

you

can

see,

the

from

the

four

stack

eight

With J key

in the sphere

Keys

~

2

I}

~

}

o

storage

formula

00

your

program.

program

Comments

These These

This

key

registers.

Jdisplayed in

A =

7Td

is

keys

square

keys

place

multiplies d2 by

Keycodes

Press

the first key

The

two stored keycode. For

09. All The number the

row,

numbers

in

that

other

first digit

of

first row

the

iii

of

on

step.

convenience,

keys

are

denotes

the

key

in

on

the

key.

program

registers, the

Surface

2

The

short

•

shown

below:

the

7T

in

the X-register.

the

program

the

right

Each

key

the

coded

by

the

row

that

row.

calculator

memory

LAST

PRGM

area

of a sphere

list

diameter.

7T.

and

the display will

15 J

of

the

on

the

digit

keys

their

of

the

key

So

15

and

that

for

the

HP-25 is

X register,

mode

, you

are

is

of

display designate

keyboard position

tells

calculated

keys

for

has a two-digit

are

coded

on

the

you

the

second

that

and

it is the fifth

the

change

00

the

key

separate

and

the

ready

to

using

area

of

to:

the

key

through

keyboard.

digit the

key

is

in

that

a

This code

1st Row

handy for

each

matrix

system

instruction

allows

without

5th Key

you

using a

to easily

reference

determine

table .

the

Merged Keycodes

To

conserve keycodes

the step. For

CZI

,

and

The

two-number display being

the

display indicate

in

that

key. Digits

is

0 0 which

(e.g., a

memory.

program for

an example the

display will

designates

displayed.

step

(Ol)

0 and 2 denote

is

~

,

Em)

Each

operation, prefixed

one step

the

prefix

of

code

the

The

two

that

of

program

the x2 function. In

III

CD

of

program

Programming

memory

this press the second key

01

step

when

and

the

change to:

01

15

that

has

number

pairs

of

the

function 0

memory.

the0key.

,ElD

)

uses

memory.

using prefixed functions,

function are merged into

02

appeared

numbers

of

program

on

CD

Digits I and 5

The

operation stored then ,

everycase,a

only

one

or

not, requires

of

the program,

the left side

memory

on

the right side

has been

denote

single

step

of

only

77

one

of

the

that

of

recorded

the

operation

program

is

0

The

keys displays keycode

Key

O

CZl

0 0

0

In

this

case, a program

three

steps

for finding

are

shown

in the display.

Display

I 01

1

02

I

03

of

program

the

area

below. Press

15

02

15

73 61

consisting

memory.

of a sphere

each

of

five

and

their corresponding

key

in

turn

and verify

keystrokes takes

the

only

78 Programming

Running a Program

Programs the

mm

execution

RUN for a The

sequentially

then

a special

are

executed

PRGM-RUN

@]@]

.

This will begin from

mode

accomplishes

diameter

operations

step 02,

and

downward

then

instruction

in

switch to

operation

press

[E§J

stored

from

step 03, and

,

mm

automatic

RUN

resets

step

the

same

in R

in

program

ste

p 00.

then

@] @]

the

calculator

00

thing.)

UN

mode

step

.

RUN

mode.

PRGM

.-D

(Pressing

Then, to run

memory

First

step

04, which

So

RUN

•

D I PRGM I

key your are

01

is

now

GTO 00

The

am

@] @]

instruction

in

keyed in

again, program memory The

instructions. Program memory was ch anged as shown following illustration.

yourself.

PRGM

mode

three-step program you keyed

It

or

in

step 04 is not an instruction you

was already there. If you press D I PRGM I

if yo u switch the calculator

is

filled with

am

in

replaced three

@]

OFF

instructions.

first

set

press

program

in

a value

program

executed

executed,

contains

and

ON

of

these

in

the

.

When you keyed in your program .

. . . program

00 01

02 03 04 05

~

47

48 49

13 00 ,

13

00 13 00 13 00 13 00 13 00

-

13 00 13 00 13 00

..

memory changed .

. from this .

t(

..

. to this.

..

00 01 02 15 03 04 05

~

47 13 00

48

49 13 00

15 02

73

61 13 00 13 00

13 00

The

illustration on the left shows after pressing ON. The

recording the

A

mID

step

go to next.

If

lator

will begin

first time.

ends

execution

If

you had

the

calculator

stored

in

the program again. Now

try

DI PRGM lin

illustration on the right shows program

three-step

@] @]

instruction

00

and

execute

~

is

pressed

executing

Each

time the

at

step 00, ready to begin again.

recorded

step

an

example.

a 49-step program, after executing

would

00.

Then

Programming 79

program

PRGM

example program.

in

the program tells the

the

automatic

again

in

automatic

instructions from

calculator

execut

e the

you would have to press ~ to

memory immediately

mode

or

turning

stop

instruction

RUN

mode ,

step

executes

automatic

00

the

stop

memory

calculator

as it did the program

instruction

the

HP-25

the

step

execute

after

to

there

calcu-

, it

49

Example.

(marble) with a surface

Press Display

2.5~

Each keystrokes

you would the time

Calculate

area

of

15.31

119.63

time you press ~ the

you

obtain

or

the tedium.

the surf

diameter

a baseball with a

have

of

recorded. You

if

you did

ace

area

1.3

Area centimeters. Area

inches .

calculator

each

of

centimeters.

diameter

of

the marble

of

the

calculate the

problem manually,

Writing a Second Program

Now

let's the programming capability you

write a

want

to write a program

second

program and use it to further

of

your

HP-25 calculator.

that

will calculate the increase

a spherical

Then

of2.5

inches.

in

baseball

executes

"cat's-eye"

calculate the

square

in

square

the

sequence

same answers

but

without

explore

Suppose

of

in

80 Programming

volume

the formula:

where

diameter. If into the X-register, the pressing the

of

a spherical balloon as its

Increase

do

is

the original

do were

keys

entered

shown

in

volume =

diameter

problem

in

1167T

of

the balloon

in

the Y -register and d,

could be solved manually by

the left-hand column

diameter

3

(d

-

1

increases

3

d

) ,

o

and

d, is the new

were

that

using

keyed

follows.

Keys

m;:zm

[]]

Ow

EiD

[]]

0

B

m

El

0

~

G

The

program switch to clear

program memory and display

list

of

keys

in

program memory steps

code

is

displays s

(Notice in

this program.

ber

3 that is the second

the new

Display

01 02

14 03

03 04 05

14 03

06 07

15 73

08

09 10 06 11

keystrokes

PRGM

above.

correct

hown.

that you had to record the

diameter

mode

The

as you key

TheBmm

that you will key

31 03

Cube

the new

21 03

Cube

the original

41

Subtract

Multiply by

61

I

Divide

71

for this problem are the same. Simply

PRGM

~RUN

step

keys

are

not

01

in

executed,

through

each

instruction by

m;:zm

instruction here se

step

of

the program from the digit s for

in

diameter

diameter.

the

cubes

.

7T.

by 6.

and press

00.

II.

Verify th at

key as an instruction

later.)

[§§C]

Then

key

but

are

each

checking

par

ate s the num-

.

in

recorded

to

the

key-

the

To

and

begin

run

the

press

execution

program

0 1

PRGM

I

from

switch to (or

ram

step

00.

automatic

@]

@])

Then

Programming

RUN

so

that

the

try

the following

modePRGM.mIl

calculator

example

81

RUN

will

.

Example.

the

Press Display 30

miim

35

[R7SJ

diameter

Find

the increase

changes

L..:

I

3~0.=00,,-----

1

8312.13

from 30 feet to

--,

Displaying Each Step

In

order

to look at this

each

step.

Two

andllm(back With

the

increase calculator and

press

0 I

to

PRGM

change

will

PressmJ

again

operations

step).

set

the

PRGM

modePRGM'-RuN

to:

program,

in

sphere

PRGM-RUN

I to

resetthe

I

01

and

the

display will

I 02 03

Now

pressllm. You

at

program

played

. Pressing Ilm again

mJ

displays

Ilm

displays

memory Of neither

.

course, because

can

memory

the

be

contents contents

stored

can

step

these in

program

in

volume

Enter

into Key run cubic

allow

volume

and

see

what

OI.Press Ilm again and

does

of

the

of

the

two

of

35

feet.

the

original

Y.

the new

the

program.

feet,

you

need

you

todo

program

switch

calculator

press

mJ

31

change

has

happened.

nothing .

work

memory.

a spherical balloon if

diameter

is

displayed.

to be able to display

this:mJ

still recorded

to

RUN

to

step

once.

to:

of

program

step

of

in

diameter

into X

and

The

answer,

(sillgle

step)

in

the

PRGM..:lRUN

00.

Then

switch

The

display

You

are

back

step

00 is dis-

memory.

program

PRG M mode,

in

82

Programming

Displaying a Particular Step

If

you

want

to

see

one

of

the

later

not

convenient.

use

the

mm

PRGM"

step

digit

PRGM~RU

displayed.

For

example

PRGM-RUN

Then

switch

will show:

When

using the

designating

press

mm

mode .

If

the first digit key following

key is ignored

Similarly, if the

mmkey

invalid key is

key

RUN

. Simply

number.

N

and

, to

switch

back

step

@]

~

one

is ignored

performed

To

display

with

press

Then

the

see

step

to

mmkey

numbers.

in

RUN

and

the

of

the

a particul ar

the

PRGM-RUN

mm

set

the

contents

lOin

RUN

PRGM

I

10

in

this

For

mode

number

two

keys

and

the

.

and

PRGM-RUN

of

the

PRGM"

mode

way, always

instance

and

mmis

is

followingmm

operation

steps

of

your

step

switch

then

key

the

specified

UN

and

PRGM~RUN.

06

, to see

then

switch

greater

keyed

program,.

of

program

in

the

switch

memory

set

to

desired

to

step

PRGM will be

program, set

press

mm

The

display

use two digits for

step 6 you

back

to

PRGM

than

four, themIil

into

the

X-register.

is

not

a digit

associated

with the

RUN

two-

the

[]]

@].

must

key

is

,

Interrupting Program Execution

From

time to time

by its

elf result. will

so

There

automatically

encountered

that

you

can

are

two

interrupt

as

program ins

will

want a program

enter

new

operations

progr

truction

data or

your

view an

H P-25

cution

on

am exe

s: ~ and D 1

to s

top

intermediate calculator when

PAUSE

execution

that

they

are

I.

Stopping Program Execution

~

works

differently

than

it

does

data

I RIS I

the

.

when

or

to write

is

then

calculator

instruction,~stops

in

new

When mode,

ward

as

pressed

program

down

pressed

continues

an

executed

from the

execution

an

from the

intermediate

keyboard

execution

Programming 83

instruction

keyboard. As

, allowing

result. in

automatic

sequentially

in a

an

you

program

executed

to

key

RUN

down-

Example Progra

needs

to cans. the

calculate

Universal

base

of

each

gram to solve this

This

program

calculates

then stops. When

program

formula

can

used

be

is:

Volume = base

The

radius

(1')

x-

and

To record

PRGM

mill

display Press

liI0 liI0

0

~

and

Y -registers, respectively,

this

program,

RUN

and

press

step

00.

Then

Display

01 02 03 04

0 05

m.

Universal

the

volumes

wou

ld also like to be able to

can

before

problem

the

after

you

restarted

the

height

Tins, a canning

of

the volume follows.

area

have

written

to

calcula

area

x height =

(h)

of

before

set the

PRGM-RUN

a I

PRGM

I to

key

in

the following list

61

74

61

02 73

Square

Place

Calculate

Stop

Calculate

15 15

various cylindrically-shaped

company,

record

the

area

One

can

into the

run.

PRGM

of

pro-

and

the

The

and

of

the

clear

the

te

the

is

base

down

the

can

program

calculated.

of

each

that

final vo l

17'r

2 x h

are

keyed

program

switch

memory

of

keys.

result,

ume.

is

to

the radius.

17'

in

X.

to

record

the area

of

the

the area.

base.

the final volume.

In

order

RUN

to run this

PRGM.mIl

program

RUN

and press a I

set

the

PRGM-RUN

PRGM

I so

that

the

calculator

switch

to

84 Programming

will begin com

plete

execution

the

table below:

from

step

00.

Then

use the

program

to

Height

25 10 ?

8 4.5 ? ?

Press

251mim

1

Radius

Display

25.00

Area

Enter

of

the

height into the

Y -register. Progr

am

10~

~

8

1

314

7853.98

8.00

.16

Imim

4.5~

~

With th e hei g

pressing ~ in aut omatic R

the

can's base;

encountered. Pressing ca

n and

In gen

display

the

final

gram

is

st

ep

00,

program

era

l, I

mor

e than

answer

more

ready

63.62

508

.94

ht

in

the

V-register

the

program

execut

RIS

I is

recorded

one

of a series,

convenient

to begin again.

~

ion

answer.

since

area

Volume Ent

Y -register.

Program area Second

UN

sto

aga

in

stops

into a

the

the calculator

stops

.

of

er

the

height into

stops to display

.

volume is

and

the

radius

mode

calculates

ps at the first

calculates the volume

at

step

00,

program when

To

display

mm

@]

Base

first can is

Volume

to display

calculated

?

the

calculated

in

the

X-register,

the

area

~

instruction

of

ready

to

run

again .

you

on

ly one

need

answer

instruction in a pro-

ends

execu

tion at

.

of

the

to or

Pausing During Program Execution

An

I

PAUSE

I in

interrupts that

do

not

about

one

can

be

used

struction executed

progr

am

exec

ution to display intermediate result s

hav

e to be

written

second,

although

mor

to lengthen the time if

in a progr

down. The

e than one I

desired

length

.

am

momentarily

of

the

PAUSE

I

instruction

pause

is

To

see how 0 1

PAUSE

Ican be used

the cylinder volume program

area

of

new program the

before the volume

the base will only be briefly displayed

is

calculated .

how different programming

the same problem. To

key

in

the program, set the

PRGM

~

RUN

and press I PRGM I to

display step 00.

Then

key

in

Programming 85

in

approaches

the following list

a program, we'll modify

the previous example. In the

This

example

will also show

can be taken to solve

PRGM-RUN

clear

switch to

program memory and

of

keys.

PRGM

Press

I1.I

w

11.1

0

o

0 1

PAUSE

This

program also assumes the height has been

Display

I 01 15 I 02 15

1

03

I

1

04

105

14

I Squares the radius

02

I Places

73

I Calculates the

61

I

74

I Calculates final volume

61

Pauses one

second.

7T

in

to show the base

X.

area

entered

in

X.

of

the base.

area

of

can.

into the Y -register and the radius has been keyed into the X-register. you have stored the instructions, set

RUN

to

PRGM'"

RUN

and press 0 I PRGM I so

will begin execution from step

the

00. Now

PRGM-RUN

that

switch

the calculator

complete the table

below using the new program.

Height

20 10

Radius

15

5

Area

of

Base

? ? ?

Volume

?

Press Display

Enter

20

Imim I 20.00

the height into the

V-register.

15

~

706.86

Area

of

base

is

displayed for

one second.

14137.17

Program stops, displaying the

volume.

l0lmim

10.00

Enter

the second height into Y.

for

If

86

Programming

Area

of

base

is

178.54

displayed for

one second.

1785.40

Program stops, displaying the volume.

Program Stops

At

times a mistake gram execution. stopped

in

the

listed below. Executing

a RIS.

gram halts program execution at the step following the Executing

Step

gram, program

Pressing

Any

Be careful to a void pressing keys during program execution. program has restart program execution in the middle

q uence within the program. gram shown below, if program number number

13

would

13

would be automatically pushed up into the

the number 4.7 would be keyed into the X-register.

of

some kind

To

help you identify why

middle

of

The

execution

00.

Whenever

execution

in

your

program will

your program, possible

of

a ~ instruction

stops

step 00

at

step 00.

is

executed

the

reasons

stop

calculator

in

a pro-

~.

in a pro-

Key. Pressing any key halts program execution.

been

stopped

appear

by pressing a key, be careful not to

of

For

example

execution

in

the display.

a digit entry key se-

in

the section

of

a pro-

halted at step 23, the

If~is

pressed

stack

pro-

are

If

, the

and

a

19 20 21 22 23 24 25 26

To

avoid problems like this, you should switch to to see

whether sequence. situation. In this

or

not you are

If

you are, you should use

case,

mode, then switch back to

~to

you can press

resume

61

14

03

Digit entry

01

Digit entry

03

Digit entry

04

Digit entry

73

Digit entry

07

15

22

in

the middle

mJorlmto

you should press 1m twice

RUN

mode and press

program execution.

PRG

of

a digit entry key

M mode

correct

in

PRGM

ED3.

the

Finally

Programming 87

Overflow Calculations.

that

by looking at the display you culator a calculation greater

caused fying the keycode

If

the result

fIJ

flow. overflow has

If

than

stops.

If

program execution stops because the result

in

the X-register

than 9.999999999 x

propriate sign.

It

is

the overflow hy switching to

in

the overflow

,the

calculator will display

Check

occurs

of

storage register arithmetic

the storage registers to see occurred.

the result

10

of

a calculation

99

-

, zero will be substituted for the

program will continue to

Improper Operation Stops. Calculations

Your

10

then

easy

the display.

in

one

of

is a number

execute

HP-25 has been designed so

can

always tell why the

is a number

99

,

all

9's

with a magnitude

are displayed with ap-

to determine the operation that

PRGM

mode and identi-

the storage registers, possibly

or

the summations with

~

to

inform you

in

of

the

which register the

with a magnitude less

number

and a running

normally .

that

cause

the word

I Error I to be displayed also stop program execution. You

identify the reason for the

PRGM

list

mode to see the

of

improper

operations

stop

keycode

can

be found

by switching momentarily to

of

the improper operation. A

in

appendix

B.

Branching

Although program execution step

executed

"branched

after

" to any

another

step

be made unconditionally

outcome

of a comparison

is

normally sequential, with one

, execution

in

program memory.

or

it

can

data

be made

values.

of

can

be transferred

The

"branch" can

dependent

on the

cal-

of

over-

can

or

Unconditional Branching

You

have seen how

you display any step

cuted

in the step step step

a program number

00

next,

in

program memory.

miD

is

used

in

program memory. As an instruction exe-

miD

is

specified.

used to

It

can tell the calculator to

as we have already

in

manual

branch

seen,

RUN

mode to help

program execution to

execute

or

to

execute

any

other

88

P'ogrammlng

Unconditional Branching

05 06

07

Execute the step specified next.

12

When recording an unconditional key with two digit keys to designate

st

ance, to branch to step 6 the program instruction must be

Em@]

~.

If

the first digit' key following

Em

key

is

ignored and the

gram memory. Similarly, if one

is

not a digit key, the

stored

in

program memory,

Example Program.

one to show tive whole tinues to

numbers

compute

number until you

the calculation overflows), where n

is

continually incremented by one,

your

friends.

press~

13 06

(GTO

06)

branch

Em

is

Em

The

number

key

following

It

is

of

the two keys following

is

ignored and the invalid key

program

calculates the squares

beginning with zero.

the square

of

the

to

stop

program execution (or until

The

simple formula used

always follow the

the

step number.

For

greater than four, the

stored

in

that

step

of

is

an interesting

of

The

consecu-

calculator con-

is:

x x n

Em

in-

pro-

Em

is

2

To and

step

key

in

the program set the mode switch to

press

0 I PRGM I to

00.

Then

key

in

the

clear

list

program

of

keys

Programming 89

PRGM

memory

shown

PRGM

and display

below.

~

RUN

Press

[QJ

BIT] _IT]

El

m

0 1

PAUSE

IT] B[±)

IT]

r.mD[QJ@]

The

program

register R

then

increments ditional gram repeated

To

gin squares

one you wish.

run the

PRGM

-.J

execution

in

branch

execution

of

the

Display

[Q

1

02

103

1

04

I 1

05

1

06

23

107

108

calcu

starting

,

I

the

at

back

with the

program

RUN

and

from

consecutive

display.

00

23

01

24

01

15

02 74 01 01

03

1

I

I I

14

51

13

late s the with zero.

contents

the

end

new

press

of

the

to

step

value in register R

set

the

0 1 PRGM Iso

step

00.

whole

Press

[E§J

Store

zero

Recall

the

squaring. Square Display

the

Increment

one. Transfer

calculate

square

of

It

pauses

the

register by

program

03

so

that

PRGM-RUN

that

Then

simply

numbers

again to

stop

in R,.

current

number

number.

square

briefty.

the

number

program

the

to

show

execution

square.

the

answer

one. The

is

used

to

transfer

the calculation

.

I

switch to

the

calculator

press

will be

shown

execution

for

in

R,

by

to

in

storage

and

uncon-

pro-

can

RUN

will be-

[E§J.

The

one

whenever

be

by

Conditional Branching

Eight different to

make

of a comparison

program answer downward.

program

decisions

execution

is

YES

, program

If

the

within a

of

data

based

answer

instructions give

program

values.

on

depending

These

the

outcome

execution

is

NO,

the

HP-25 the ability

on

"conditionals"

of

the test.

continues

the

calculator

the

outcome

transfer

If

the

sequentially

branches

90 Programming

around the follow ing step , which can contain an uncondition

br

anch

or

a simpler instruction

(EmJ

for

example).

The

pro-

gram makes a decision for you! '

Conditional

I--------I~

The

I n each case, the tests are ma

two-digit

Test

~~~

..)

eight different conditionals

exponents

actually stored

Program around to

in

de

the

execution

one

test

is

step

NO.

branches

if

the

answer

your H P-25 are shown here.

on the 10-digit

in

the stack registers , not

number

s and

on the displayed values.

x<y

l tests to see if the value

D I

the value

in

the Y-register.

D Ix"yl tests to see if the value

or

equal to the value

D

lRtil

tests to see if the value

in

the value

D

~

value

iii

18I tests to see if the value

the Y-register.

tests to see if the value

in

the Y-register.

in

the Y-register.

in

the X-register

in

the X-register

in

the X-register

in

the X-register

in

the X-register

is less than

is

greater

is

not equal to

is

equal to the

is

less than

than

zero .

iii

Inol tests to see if the value

or

equal to

iii l

uol tests

zero

.

to see if the value

in

the X-register is

in

the X-register

greater

is

not equal

than

to zero.

iii

rx=oJ

tests

to see if the value

in

the X-register

is

equal to

zero .

al

Example Program.

input value

x (x must

This

program calculates the arc sine

be

within the limits program tests the resulting angle, and if it zero ,

adds

360 degrees to it.

The

angle displayed by the pro-

gram , then, is always positive. To

key

in

the program

and pressD I

00.

Then

key

PRGM

in

set

the mode switch to

Ito

clear program memory and displa y step

the following list

of

keys.

of

- 1 and + 1) .

is

not

greater

PRGM

~

of

The

than

an

RUN

Programming

91

Press

m

~

m

§]

mIiJ@J@J

@]

~

@J

[±]

To

run the program set the

PRGM

.mil

gin

execution

values for

Press Display

m

~

. 5

[R?S]

. 5

rmJ

[E§]

Display

01 02 03

04

I

05 06

I

07

I

RUN

and press D I

from step 00.

x.

The

15 15

13

resultant arc sine will always be positive .

Calculates the arc sine .

04

Compares

51

If

00

03 06

00

51

greater

sine.

'}

Oth"w;"

I add I 360 degrees I to the arc sine.

PRGM-RUN

PRGM

I so

that

Then

key

the result to zero .

than zero, display arc

switch

the calculator will be-

in

I 0.00 Set degrees mode . I

30.00

:=1

-=0~.5

~~

I

330.00

==~

Arc

sine of.5 equals 30 degrees .

Key

in

negative value for x .

360 is added to a positive angle .

back

positive

the

arc sine to give

or

Editing a Program

Even

the

most

grams .

These tions to mistakes occur

they need to be found and designed to make this error-checking process as possible.

experienced progra

errors

range from mistakes

in

recording the program.

Finding the Error

One

of

the easiest ways to find

is

to

work

properly answer

or you have a program formula value

SST

will seldom pinpoint the mistake. down program

In

the

area

of

I for r will give an

Execution.

RUN

mode ,

a test

answer

can be easily determined.

that

calculates the

=

7T

X

r2

, you can easily determine that an input

In

longer programs a wrong test-case

execution

the_key

by using the mil key

case

answer

will

out

in

For

execute

mmer

finds

errors

in

the original equa-

corrected, and

if

your

which you

area

of

7T

these cases, you can slow

Wherever

the HP-25

program

either

For

of

.

your program instruc-

example , if

a circle using the

in

RUN

to

RUN

negative

in

his pro-

they

easy

is

working

know the

answer

mode.

is

as

92 Programming

one

tions mode, the

When

mJ

familiarize

at a time.

program

you release

on the simple

yourself

themJkey,

When

step

area

of

with its

you hold

number

themJkey

and

keycode

the instruction is

a circle program

operation.

down

in

are

RUN

displayed.

executed. Use

shown

below to

Example Program.

circle using

the

PRGM-RUN

I

PI<GM

I to

clear

in

the

list

of

keys

This

formula: A =

switch to program

shown

PRGM

memory

below.

program

'TTr2

where

and

calculates

r is

display

the

step

PRGM~RUN

Press Display

15

run

PRGM"

02

15 73

61

that

the

program ,

a value

RUN

and pressD

forr

set

has

been

the

PRGM-RUN

~

1

m 0

m

El

01

1 02

0 1 03

The

program

X-register.

back

to

To

RUN

assumes

through the program in slow motion using a value

Press

10

miD

Display

1 10.

1

01

15

02

1

100.00

1 02 15 73

3.14

03

61

When

you hold

first instruction When

you release

is

instruction Again

the

second

Again

second

executed.

holdingmJdown

instruction.

releasingmJexecutes

instruction.

HoldingmJdown

mJdown,

is

third instruction this time.

1

314.16

releasing

mI

And third instruction.

You

can see

gram using

that

it would be

themJkey

easy

to

spot

a mistake

.

the

area

radius .

and

00.

keyed

Set

press

Then

into

switch

.

Now

of

10

for r.

the

displayed.

mJ,

the

displays

executes

in

your

of

the

key

the

step

first

the

pro-

a

When

you hold

step

number

When

you

ever

if

you previous mode

after

from

the

RUN

mode

program.

Press

1m

If

you

displayed

and

release

switch

step

pressing

Display

03

I

314.16

I

02

1

314.16

now

switch

:

thelm

keycode

1m, the X

back

is

now

step

15

to

1m, the

key

down

in

for the

to

displayed. And

in

program

61

73

PRGM

I

02

PRG M mode,

calculator

memory.

program

Holdinglmdown mode instruction

Releasing the original X-register. Again holding plays program

And

releasing 1m displays the

original register again.

mode

15

73

Programming

RUN

mode,

step

is

again

you

if

you

press

will begin

instructions

displays

the

.

the

1m key displays

contents

1m

the

contents

the

second

the

program

are

displayed.

displayed. How-

will find

Now

[R7SJ

in

execution

press

of

the

in

RUN

the

down

step

in

of

the

step

that

RUN

1m in

above

dis-

X-

will be

93

the

Cued Stops.

during each

stop before execution can

look number" contains numbers I through 8 appear quired editing a

If

execution

by

recording

each

[R7SJ

because

at

the

for

the

eight

stops

each

time.

program

you

have a program

for

data

entries,

a familiar

instruction.

of

the ~ instruction

displayed

required

These

.

for

data

identification

X-register input.

Then

For

inputs,

so

you

that

you

may

number

when

to

example

it

may

know

numbers

is

halted

several

want

to

into the

the in

see

the " identification

be helpful to

which

program

calculator

the

program,

if

your

input

are

"identify"

times

just

stops

you

program have

the

is

re-

helpful in

94 Programming

If

you key in

remember

entry. Thus,

digit the

program are less you resume program immediately

data

that

press

running

after

resuming program

the calculator will

part

of

mIim after you key in

the

program, or

after

the program has stopped running,

execution

the

number

the ~ instruction .

you

there

assume

have

the

data

is

does

that

just

and before you

an

Changing One Instruction

Changing your the

ram

changed .

need to display step 05. press and replace the incorrect information already stored

If

operation).

any operation here.

Example Program.

signed to take the Press Display

mIim 1

[2]

m

D

Suppose however take-ridden program :

Press

mIim

[2]

m ~

mJ

D

or

HP-25 calculator

error

in

step

[KJ

CZl

correcting one

has been found , use

RUN

mode to display the step

For

example, to change the instruction

the

correct

06

is

an

This

01 102 03 1 103' 15 221 104

that

, you discover you have keyed

Display

1

01

1

02 03

1

03

104

105

because

If

key

or

keys for step 06.

extra

step

instruction tells the calculator not to perfo rm

The

cube

root

311

14

031

upon

reviewing the program with the

31 1

1

15

211

14· 03

1

step

of

your

ofthe

mJ

you wish to change the step, simply

in

your

program

of

a number.

Oops! key.

And mistake .

program

features built into it.

or

mJ

in

PRGM

preceding

They

will write

program, press m

represented

in

the following mis-

You

pressed

you

pressed

it aga

not

terminat

the digits in

keyed in un-

mIim

in

the

is

easy

with

Once

mode

the step to be

step 06, you

over

in

that step.

~

(no

below

is

de-

mDkey

the wrong

in

by

e

or

,

Set

the

PRGM-RUN

1

PRGM

I,

and key in this mistake- ridden second program now.

To

correct

02.

Then

for step 03.

Programming 95

switch to

PRGM

PRGM~RUN

, press a

the program, press mJ three times to display step

correct

the first mistake

by

keying

in

the

correct

keys

Press

With step

Since this

Display

First

102 103

03

displayed you are ready now to

is

an unwanted

15

031

22

1

extra

display this step.

Then

press the

step

03.

step , use the iii

correct

~

to replace its contents.

Press

Display

103 15 221 104 15 74 1

Display step Press

lillNop

03

to correct step 04.

lso that the calculator will not perform an operation here.

Now

set

the

PRGM-RUN

and press a 1

PRGM

I to reset the calculator to step 00.

ample below will help you determine whether

switch back to

RUN

or

not you have

PRGM

corrected the program.

Example. Find the cube root

Press

8

ffiZ§J

1251

RIS

Display

1

2.00

I

1

5.00

of

8 and then

of

125.

Adding Instructions

If

you have recorded a medium-sized program and have left

a crucial sequence

have to recorded

start

in

can then use the

sequence when tional branch back to the main part of

the sequence.

of

over.

keystrokes right

The

missing sequence

in

the middle, you do not

of

keystrokes

the available steps following your program.

miD

key to make an unconditional branch to the

it

is

needed and then make a second uncondi-

of

your program

keys for

step 04.

function

-.J

The

out

can

You

at

the end

RUN

ex-

be

96 Programming

The

program seg

ear.

Thre

cl

00 01 02 03 04 05 06 07 08

In

order to add the missing step s we need to branch to one

a va

program is shown below.

00 01 02 13 10 03 04 05 06

07 08

13 00

il

ab le pro gram ste ps

13 00

ment shown

e ke ys are miss ing be

21 51

,

22

21

Missing and Em]

in

program memory. The co rrected

Branch to

step

10

~

22

Branch

to

step

back

03

belo w should make this more

twe

en s

tep

s 02 and 03.

thr

ee

steps ( 0 ,

[§J

) here .

Step

02

~

10 11 12

L

13 14

51

14 02

32

23

06

13 03

Missing

}

Keys

mIll

of

the

Notice

in

particul

02 is n

ow

ti

onal branch ins

in

steps

II

co

nditional branch back to step 03

un

ar that the instru ction originally stored

stored

in

step

10.

thr

truction

ough

to ste p

13

and the instru ction st

Step 02 n

ow contains an unco

10. The missing keys are stored ored in

in

the main program.

step

14

in

step

ndi-

is an

HP 25 Owner's Handbook Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Contents

Function Key Index

H P-25 Memory

Programming Key Index

Manual Problem Solving

Programmed Problem Solving

Getting Started

Display

Keyboard

Negative Numbers

Clearing

Functions

One-Number Functions

Two-Number Functions

Chain Calculations

A Word About the HP-25

Controlling the Display

Display Control Keys

Fixed Point Display

Scientific Notation Display

Engineering Notation Display

Automatic Display Switching

Calculator Overflow

Error Display

The Automatic Memory Stack

The Stack

Initial Display

Manipulating Stack Contents

Reviewing the Stack

Exchanging X and Y

Clearing the Stack

One-Number Functions and the Stack

Chain Arithmetic

Order of Execution

Constant Arithmetic

Function Keys

LAST X

Prefix Clear

Number Alteration Keys

Reciprocals

Square Roots

Squaring

Percentages

Storage Registers

Trigonometric Functions

Polar/Rectangular Coordinate Conversion

Logarithmic and Exponential Functions

Statistical Functions

Vector Summations

Programming

Why Write Programs?

Three Modes of Operation

Introductory Program

Running a Program

Writing a Second Program

Interrupting Program Execution

Branching

Editing a Program