HP HP-42S User Manual

An alternative HP-42S/Free42 Manual

(Version 0.6)

2005

Author: José Lauro Strapasson, Brazil.

[e-mail]

http://joselauro.com/42s.pdf

Index

Index
1 Introduction
2 Basic Operations
3 Memory
4 Probability
5 Complex numbers
6 Programming
7 Using the Solver
8 Numeric Integration
9 Statistics
10 Matrices
11 Other Bases
12 Flags

License for this manual

1 Introduction

Since HP-42S was a very nice calculator, and its official manual is no longer freely available and
there were many people looking for its manual, seemed good to me to write my own HP-42S
manual. I personally don't have a HP-42S (more than U$300 on ebay). I have a HP-33S and had a
HP-48G, but my brother has one and I also use Free42 simulator for PalmOS.

This manual can interest people who:

a) Have a HP-42S calculator and lost its manual.
b) Got the Free42 simulator and want to know how to use.
c) Have a palmtop with PalmOS and want a nice scientific calculator (get Free42)
d) Just want to have an idea how 42S was.
e) Have the official manual but don't want to read more than 300 pages!

Why HP-42S? Because it was a very, very nice calculator and also a powerful one. I know some
other HP models from the past and the present like 48G, 49G, 28S, 33S, 20S, 6S Solar, 15C, and
even a TI-36X Solar, etc, but 42S is my favorite. And because there is a free simulator (Free42) that
works on Palm OS, Windows and Linux and there are also some emulators (at the moment
emulators are only useful for who has a real calculator since HP-42S roms are not freely available).
This calculator played an unique position among HP calculators! Being a scientific programmable
100% RPN calculator, it also had some graphing abilities but was pocketed sized and non RPL
(some people as me like RPN, but dislike RPL).

It is important to say that this manual is not complete and I don't want it to be. Two things I really
don't want to see here are PRINTING and HP-41 compatibility. This because I suppose most owners
don't have the printer (and it is not so useful) and also haven't had a HP-41 prior to HP-42S.

If you want to download the fantastic Thomas Okken Free42 program please go to this web site

http://home.planet.nl/~demun000/thomas_projects/free42/

In my opinion Free42 is even better than the real HP-42S. Try asin(acos(atan(tan(cos(sin(6°)))))).

For more information about HP-42S please see

http://www.hp42s.com
http://www.hpmuseum.org/hp42s.htm

Here you can find emulators for HP-42S

http://privat.swol.de/ChristophGiesselink (very nice)
http://www.geocities.com/hrastprogrammer/HP42X/index.htm

I would like to finish this introduction saying that would be nice to have HP-42S back to life again
and even better to have a model (both real and in simulator/emulator form) based on HP-42S but
with some of the 33S features like more memory and equation editor, fractions, program lines
starting with letters, physical constants, units conversion, less useless functions, etc. And also would
be nice to have HP-42S roms for free just like what happened to HP-48G and other models and
keeping PDF versions of the manuals of retired models to download would be nice too. Perhaps
someone listen to me! :)

2 Basic Operations

2.1 RPN

HP-42S as most old HP calculators was a RPN calculator. RPN comes from “Reverse Polish
Notation”. In RPN we first enter data and then we enter the mathematical operations.

Example: To make a simple operation like 2+2 in a normal algebraic calculator we do
2 + 2 =
which give to us 4.

To make this using a RPN calculator we do
2 ENTER 2 +

As we can see in RPN mode we first enter the data pressing the ENTER key after every data (except
for the last in HP's RPN) and then we enter the operations.

Lets now consider the following calculation
4+(2x79).

In a RPN calculator we do
2 ENTER 79 x 4 +

But how one could do this in an algebraic calculator?
If the calculator has the ( and ) sings it is just do
4 + ( 2 x 79 ) =

But if there are no () we do this in a good calculator by doing
4 + 2 x 79 =

By a good calculator we mean a calculator which knows that x and / are prior to + and -.
In a bad algebraic calculator which does not know this we have to do
2 x 79 =
and
4 + =
or
2 x 79 + 4 =

What about calculate sin(33)? In a RPN calculator it is just do
33 sin
or if you prefer
33 ENTER sin
(in this case we don't need to press enter key)

But in an algebraic calculator we have two ways.
In the classic old models it is like RPN and we do
33 sin
but in some modern models (which typically allow you to edit entered data using cursors) we do
sin 33 =

So algebraic calculators are ambiguous because the many ways they work. RPN calculators are
more standard and so less ambiguous.

The main key to understand how to use RPN in more complex calculus is to realize that in RPN we
make calculations from “inside” to “outside” instead of from left to right.
Example:

8 x ln[5+sin(40)] in RPN is doing by

40 sin 5 + ln 8 x

In RPN we can make any calculation we do in algebraic devices and this is not only more elegant
but also more effective since there are less ambiguity's and we use less key strokes.

For example, my HP-33S, which is both algebraic and RPN, is always in RPN mode. (Just to insert
equations I think algebraic mode is better)

For more information on RPN, please see http://www.hpmuseum.org/rpn.htm

2.2 Turn ON/OFF

To turn your HP-42 on press ON. The ON key is the same EXIT key.

To turn your HP-42S off press ▀ OFF. OFF is in the same key of EXIT and ON, and by ▀ OFF we
mean you have to press the orange key before press the EXIT key which have OFF in orange above.
The orange ▀ key is what in some other calculators is called “second function”. When you press this
all keys turn in what is written in orange above it.

Actually ▀ OFF is a redundancy since OFF can be only accessed by pressing ▀ first. But (as in HP­42S official manual) we will do this just to remember when we have to press ▀ or not. If you press
this key a second time all keys go back to the normal function.

2.3 Setting the display contrast

HP-42S, as most HP calculators, can set the display contrast by pressing at the same time ON and +
or -.

2.4 Training RPN using HP-42S

Now that you have your 42S on try to do the following calculations:

1) 6x(4+3).

Answer
4 ENTER 3 + 6 x

2) 2+{2x[2+(2/2)]}

Answer
2 ENTER 2 / 2 + 2 x 2 +

IMPORTANT: For sake of simplicity sometimes we will use / instead of ÷.

2.5 Menus

Not all functions of HP-42S are visible above the keys. It has menus with much more functions. The
menus are

ALPHA, MODES, DISP, CLEAR, SOLVER, ∫f(x), MATRIX, STAT, BASE, CONVERT,
FLAGS, PROB, CUSTOM, PGM. FCN, PRINT, TOP.FCN and CATALOG.

2.6 DISP Menu

The DISP menu is the first menu we have to see. It is above E key. So start by pressing ▀ DISP.
When you do this the DISP menu appears in the first line with the following functions.

FIX, SCI, ENG, ALL, RDX., RDX,

These functions appears just above ∑+, 1/x,√x, LOG, LN and XEQ. Now with DISP menu active
those keys don't represent their original functions but those of DISP menu. The same happens with
all menus.

2.6.1 The FIX function.

The FIX “function” is not a function in the mathematical sense, but a calculator function. By using
FIX function the display becomes with a fixed number of digits after decimal point.
Ok, press FIX. (I mean ∑+ with DISP menu active)
When you do this what appears is
FIX _ _
Then you have to enter a number up to 11. Example
FIX 0 4 set calculator to have 4 digits of precision after the decimal point. A number like π will
appear as

3.1416

and √2 will appear as 1.4142.
(You can verify this by doing ▀ π and 2 √x respectively)

If you put FIX 0 9 than those numbers will appear as

3.141592654

and

1.414213562.

It is important to say that this is not the actual precision the calculator will have but just the display
precision. To see all calculator precision you have to press ALL in DISP menu (above LOG key).
By doing so those numbers will appear as

3.14159265359

and

1.41421356237

As you can see the numbers are not truncated but rounded.

Not all numbers can be seem with a fixed decimal precision. If you put 4 digits for fixed precision
the number π will appear as 3.1416 but if one calculate

10

8

(do this by doing 8 ▀

10

x

) what
you are going to see is 100,000,000.000 with 3 decimal digits. This happens because the calculator
cannot show more than 12 digits at a same line.

2.6.2 The ALL function

We already talked about ALL function. It makes the calculator to show all of its precision.

2.6.3 The SCI function

The SCI function works just like FIX one but puts the calculator in “scientific” mode. The numbers
will be shown as a decimal number between 0 and 1 times a power of 10.

For example 1000 will be represented as 1.00E3 with you put the calculator in scientific mode with
2 digits. 1.00E3 means 1.00x

10

3

. The π number will appear as 3.14E0.

Actually even when in FIX mode the calculator will turn in scientific notation to give some answers.
For example if you calculate 1.0001-1 with FIX 3 you are not going to get 0.000 but 1.000E-4. This
means that the calculator is “smart” and show the result in the best way as possible.

Exercise. Show that 1.0001-1 gives 1.000E-4 in FIX 3 mode.
Answer:
First we put the calculator in FIX 3 mode by doing ▀ DISP FIX 0 3.
Then we do 1 . 0 0 0 1 ENTER 1 – and we get the answer.

As you can see when you are in FIX mode a sign ■ appears on the right side of FIX name in the
DISP menu. This means FIX mode is active. The same happens with SCI, ALL, etc.

It is out of our scope to give a full description of scientific notation. In case of need please report to
a first book of physics for high school or college.

2.6.4 The ENG function

The ENG function puts the calculator in engineering notation. It looks like scientific notation but
now the first number does not need to be between 0 and 1 but can be between 0 and 1000 and the
power will be always 3 manifold.

Example: 100 will be represented by 100.E0 in ENG 2 mode while 1000 will be 1.00E3 in the same
mode. Why do we get 100.E0 for 100 instead of 100.00E2 in ENG 2 mode? Because the calculator
shows in engineering mode the same number of digits it shows in scientific mode.

2.6.5 RDX. And RDX, functions

In some countries like Brazil we use ',' for decimal point instead of '.' and also '.' instead of ',' for
1,000 and 1,000,000 etc.
For example π is written here (Brazil) as 3,141 etc and not as 3.141 etc. In FIX 3 mode one million
is written here as 1.000.000,000 and not as 1,000,000.000 as in English use. By pressing RDX, you

make the calculator to use ',' for decimal point and by pressing RDX. we make it use '.' for decimal
point. Again the active mode is followed by a ■ sing. Here, in this manual, I suppose the calculator
using '.' for decimal point.

2.6 MODES Menu

To access MODES menu just press ▀ MODES. (MODES is above +/- key).

DEG actives degree mode for trigonometric functions. In this mode a circumference has 360
degrees. RAD actives radian mode and in this mode a circumference has 2π radians or just 2π.
GRAD is not so useful and correspond to 400 degrains for a circumference.

For example: In degrees we have sin(90°)=1 and in radians we have sin(π/2)=1.

Try this: ▀ π 2 / COS in radians mode. Why the result is not exactly zero?
Answer: Because the number that calculator entered was not exactly π but 3.14159265359.

REC actives rectangular mode (x,y) and POLAR actives polar mode (r,θ). We will see this more in
detail when study complex numbers.

The MODES menu has another line but we will discuss this later. We will discuss the others menus
later too.

2.7 The Stack

No calculator can store an infinite amount of data. In algebraic calculators the “( )” are limited to a
given number depending on the model. The same happens in RPN calculators. In some models like
HP-48 or HP-49 the amount of input data is limited only by available memory. But in other models
like 32SII, 33S (in RPN mode) and 42S the input data have to fit in a “stack” of four lines.

There are four lines labeled x, y, z and t. (actually the name of the last two is not so important).
So the stack is something like

t:0.0000
z:0.0000
y:0.0000
x:0.0000

But as the calculators display has only two lines just x and y lines are visible.
When you enter a number (say 2 ENTER) what happens is the following.

i) The content of lines t and z are lost.
ii) The content of line y goes to line t.
iii)The content of line x goes to line z.
iv)The content just entered goes to line y and line x.

So what you just entered appears twice. So if you do 2 ENTER + you will have 4 as answer.

This is a feature, a bad feature I think, of the HP RPN style of 42S (also in 33S, 12C, etc but not in
HP48 or 49). In my opinion we could have a simpler RPN style. Anyway there is another way to
enter data in RPN. It is just type what you want and press the desired function key.

For example, if you do 2 1/x before the 1/x function the calculator makes an automatic enter but in

this case the content just entered appears only once.

So if you do 2 1/x or another example 9 √x what you will have will be

i) Only the content of the line 4 (line t) will be lost.
ii) The content of line 3 (z) goes to line 4 (t).
iii)The content of line y goes to line 3 (z).
iv)The content of line x goes to line y.
v) Your result will be in the first line x.

This second way to enter data looks more intuitive to me and I think it should be aways like this.
But it is not!:( So to do 2+3 we have to do

2 ENTER 3 + (and not 2 ENTER 3 ENTER +).

(Actually one can also use EXIT to enter a number without duplication)

If you just press ENTER you duplicate what is in line x.

When making a calculation one should never forget about the limitation of the 4 lines of the stack.

The lines of the stack cannot contain only numbers but also matrices, complex numbers, etc.

The basic operations with the stack are: x><y and R↓. The first changes line x with line y. The
second makes the stack rolls down (line y goes to line x, line x goes to line t, line t goes to line z
and line z goes to line y)

In the CLEAR Menu there are some interesting functions: CLST which clears all the stack
(something missing in HP-33S). CLX clears the line x in the same way of pressing ←.

The ← is more used to correct a number when typing it.

Another useful function is ▀ LASTx which gives the last calculated result.

2.8 Getting used to some keys of the keyboard

Let's discuss some basic keys of the calculator. We will start from superior left side.

Σ+ and ▀ Σ- : These are statistical functions. We will discuss this later.

1/x and ▀

y

x

: 1/x just calculate the inverse of a number which is in line x.

▀

y

x

is the potential function. To calculate

5

3

= 5.5.5 we do

5 ENTER 3 ▀

y

x

.

√x and ▀

x

2

: These functions just calculate the square root and the square of a number in line x.
When studying complex numbers we will see that unlike HP-33S in HP-42S the
number in square root can be negative.

LOG and ▀

10

x

: These functions calculate the base 10 logarithms and it's inverse.
These things were important before the era of calculators so there is no reason
to have them in one.

LN and ▀

e

x

: These functions calculate the base e=2.71828... logarithm and it's inverse.

Unlike LOG these are very, very important functions!

But what about if we want a logarithm in another base? It would be nice to have a special key for
this but it is just about remembering that

logxy=logzy/ logzx

where z is any other base.

If we take z=e=2.71828... we have

logxy=ln y /ln x

.

Example: Calculate

log28

Answer: 8 LN 2 LN / which give us 3 because

23=8

.

XEQ and ▀ GTO: These are related to programming and we shall discuss this later. XEQ will also
be discussed in ALPHA menu part.

STO and ▀ COMPLEX : These are related to the memories and complex numbers. We will
discuss this later.

RCL and ▀ % : RCL is related to memories and we will discuss later. ▀ % is the percentage
function. To calculate 10% of 300 we do

300 ENTER 10 ▀ % which gives 30 as answer.

Note that 300 remains in line y, so if you want to calculate 300 plus 10% you do

300 ENTER 10 ▀ % +

R↓ and ▀ π : We already discuss these. The first rows down the stack and the other returns
π=3.14...

SIN and ▀ ASIN : These are the sinus trigonometric function and its inverse. The angle type is set
up as said before in MODES menu. The default is degrees. ASIN is the inverse
usually called arcsine or sometimes

sin

−1

. (don't confuse with cosec which is
1/sin). It is important to remember that ASIN is not a real function since there is
no single result. For example sin(135°)=sin(45°)=√2/2 but the calculator gives
always ASIN(√2/2)=45°. HP-42S will give a complex number if the input of an
arcsinus is bigger than 1 or smaller than -1.

COS and ▀ ACOS: These are the cosinus trigonometric function and its inverse.

TAN and ▀ ATAN: These are the tangent trigonometric function and its inverse. Not all numbers

can have a result for tangent. For example tan(90°) goes to infinite. The
HP-42S gives a big number instead.

ENTER and ▀ ALPHA: The ENTER key does not need any comment. ▀ ALPHA is the alpha­ numeric menu used to enter letters instead of numbers. When you press ▀
ALPHA what appears is