HP 30B User Manual

HP 20b Business Consultant HP 30b Business Professional Financial Calculator User’s Guide

HP Part Number: NW238-90001 Edition 1, December 2009

Legal Notice

This manual and any examples contained herein are provided "as is" and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, noninfringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual.

Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein.

Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws.

Hewlett-Packard Company 16399 West Bernardo Drive MS 66M-785 San Diego, CA 92127-1899 USA

HP 20b Business Consultant

iii

HP 30b Business Professional

Keyboard Map Legend

Number Feature Number Feature

1 2-line, alphanumeric scrolling

2 Time Value of Money keys

3 Cash Flow, IRR and NPV keys 11 Backspace key/Reset menu 4 Data and Statistics menus 12 Percent/Percent calculation

5 Input key and Memory menu 13 Recall and Store 6 Insert and Delete/scroll (up

7 Shift key 15 Amortization/Depreciation

8 On/Off/Cancel 16 Annunciators

* Only applies to HP 30b. **Does not apply to the HP 20b.

display screen

(TVM)

and down)

9 Common Mathematical

functions and Math (Math)

10 Program menu*

RPN Swap/Close parenthesis

(business) and Date menus

14 Black-Scholes** and Bond

menus

Legal Notice.............................................................................................................ii

HP 20b Business Consultant ......................................................................................iii

HP 30b Business Professional .................................................................................... iv

Keyboard Map Legend.............................................................................................. v

1 Basic Features ......................................................................................................... 1

Welcome to your new HP Financial Calculator .............................................................1

Turning the Calculator On and Off..............................................................................1

Selecting a Language ................................................................................................1

Adjusting the Display Contrast ....................................................................................1

Cursor .....................................................................................................................2

Two Line Display.......................................................................................................2

The Mode Menu: Setting Preferences...........................................................................2

Changing the Calculation Mode .................................................................................4

Key Presses, the Shift Key, Secondary, and Tertiary Functions*.......................................4

Annunciators ............................................................................................................6

The Input Key ...........................................................................................................6

The Equals Key .........................................................................................................6

Using the Input and Equals Keys .................................................................................6

Editing and Clearing Entries .......................................................................................7

The On/CE Key........................................................................................................7

The Reset Menu ........................................................................................................7

Notes about Special Menus .......................................................................................8

Memory and the Memory Menu..................................................................................8

Accessing Menus and Menu Maps..............................................................................8

2 Mathematical Calculations ..................................................................................... 11

Mathematical Functions ...........................................................................................11

Number Entry and Display.......................................................................................11

Chain Mode...........................................................................................................12

Algebraic Mode .....................................................................................................12

Reverse Polish Notation (RPN) Mode .........................................................................13

The RPN Stack........................................................................................................13

Last Number...........................................................................................................14

One-Number Functions and the Math Menu ...............................................................18

Random number .....................................................................................................19

The Math Menu ......................................................................................................19

The Probability Sub-menu.........................................................................................21

Binomial Functions ..................................................................................................23

Two-Number Functions ............................................................................................23

Storing and Recalling Numbers ................................................................................24

Recall Arithmetic .....................................................................................................24

Storing and Recalling with Time Value of Money (TVM) Keys .......................................24

Recalling a Menu Item Value in a Menu.....................................................................25

Recalling and Storing Values in the Data and Cash Flow Menus...................................25

Rounding Numbers .................................................................................................25

Percentages............................................................................................................25

3 Time Value of Money............................................................................................. 27

Time Value of Money (TVM) Keys..............................................................................27

Amortization.......................................................................................................... 29

Interest Conversion Menu ........................................................................................ 33

4 Canadian Mortgages: TVM Canada........................................................................35

Canadian Mortgage Example.................................................................................. 36

5 Cash Flows ............................................................................................................37

Cash Flow Example ................................................................................................ 38

Sample Cash Flow Diagrams ................................................................................... 46

6 Bonds....................................................................................................................47

The Bond Menu...................................................................................................... 48

7 Black-Scholes Calculation Menu* ............................................................................51

The Black-Scholes Menu ..........................................................................................52

8 Date Calculation ....................................................................................................57

The Date Calculation Menu...................................................................................... 57

9 Break-even ............................................................................................................59

The Break-even Menu..............................................................................................59

10 Business Problems................................................................................................61

The Percent Calculation Menu.................................................................................. 61

11 Depreciation ........................................................................................................65

The Depreciation Menu ........................................................................................... 66

12 Statistical Operations ...........................................................................................69

The Data and Stats Menus ....................................................................................... 70

13 Programming.......................................................................................................75

Programming the HP 30b ........................................................................................ 75

Key Presses for Program Instructions.......................................................................... 75

Programming Example ............................................................................................ 77

Program Step 0...................................................................................................... 78

Reassigning Menu Functions ....................................................................................79

The Program Menu and Program Editing ................................................................... 80

Tests and Jump Functions......................................................................................... 81

Long Programs and Battery Life ................................................................................ 82

Sub-Function Call.................................................................................................... 82

Other Programming Functions .................................................................................. 83

Messages..............................................................................................................84

Debugging a Program.............................................................................................85

Saving, Restoring, and Modifying Mode Settings ....................................................... 86

Solve .................................................................................................................... 87

14 Error Messages ....................................................................................................89

Error Messages and Calculator Status ....................................................................... 89

15 Warranty, Regulatory, and Contact Information ....................................................91

Replacing the Batteries............................................................................................91

HP Limited Hardware Warranty and Customer Care................................................... 91

Contact Information ................................................................................................ 95

1Basic Features

Welcome to your new HP Financial Calculator

This manual is designed to familiarize you with the many features available on your new HP Business and Financial calculators. It includes menu maps, cash flow diagrams, and example problems and solutions with key presses and screen shots. Also included are sections which list the error messages, a chapter about programming, and an explanation of how Reverse Polish Notation (RPN) works. Refer to the Table of Contents for quick access to various topics. If you need more information about your calculator or calculator operation, please refer to the training materials available at: www.hp.com/calculators.

This manual describes in detail the features available on both the HP 20b and the HP 30b calculators. In addition to all of the features found on the HP 20b, the HP 30b includes the Black-Scholes option pricing model, Modified Internal Rate of Return (MIRR), Financial Management Rate of Return (FMRR), and programming capabilities. When features apply only to a particular model, they will be identified throughout the manual with an asterisk*.

Turning the Calculator On and Off

To turn on your calculator, press O. To turn it off, press :a.

Turning the calculator off does not erase any data. The calculator automatically turns itself off after approximately five minutes to conserve energy. If you see the low battery symbol ( )

in the display, replace the batteries. See the Chapter 15, Warranty, Regulatory, and Contact Information for instructions on replacing the batteries.

Selecting a Language

English is the default language for messages displayed on the screen. To select a language other than English:

1. P r e s s

2. Press

3. Press

4. Press O to return to the default calculator screen.

5. For more information on accessing menus and changing calculator settings, refer to the

:u to access the Mode menu. FIX displays on the top line of the screen. <

repeatedly until English displays on the screen.

I until the desired language is displayed. The displayed language is the

active setting.

section below titled, The Mode Menu: Setting Preferences.

Adjusting the Display Contrast

To adjust the contrast of the display, press and hold O while pressing the + or - keys. Each press of the + or - keys slightly increases or decreases the contrast of the

display.

Basic Features

Cursor

When you enter a number, the cursor (_) blinks in the display and indicates you are in number entry mode.

Two Line Display

There are two lines in the display screen as shown in Figure 1.

Figure 1 Display Screen

The top line of the screen displays operation status, operator symbols, annunciators, and abbreviations of the variables and menu names. Throughout this manual, this line is referred to as the top line. In Figure 1, SIN is on the top line. The bottom line displays numbers you have entered, or results. Throughout this manual, this line is referred to as the bottom line.

When no operations have been entered and no operations are pending, the bottom line of the screen displays 0.00. This state of the calculator is referred to as the default calculator screen.

The Mode Menu: Setting Preferences

The Mode menu allows you to customize the calculator. To access the Mode menu, press

:u. Press < or > repeatedly to scroll through the menu starting with FIX=2

(the number of digits displayed to the right of the decimal point). Once an item is displayed,

press I to cycle through the other options for that setting. To exit the Mode menu, press O. Table 1-1 lists the items in the Mode menu.

Basic Features2

Table 1-1 Mode Menu Settings

Setting (top line) Description

FIX= 2 Display precision (number of digits displayed to the right of the decimal point).

Default is 2.

Key in the number of digits you want and press I, or press = until the

number of digits you want is displayed. The display precision can be any number from 0-11. If you specify –1, the calculator

displays numbers with the most appropriate number of digits after the decimal point.

If you find you need to change the FIX setting often, use the following shortcut:

1. P r e s s

2. Press : again, and, without releasing it, press a key, 0 through 9 that

Degree or Radian Angular mode in degrees or radians for trigonometric functions.

Default is Degree.

Pressing I toggles between these options.

Date:

mm.ddyyyy or dd.mmyyyy

1. 23 or 1,2 3 Selects point or comma as decimal separator.

Format for dates. December 3, 2010 is entered as 12 .0 32 010 in mm.ddyyyy format, or

3.122010 in dd.mmyyyy format. Note the (.) in both formats separating the first and second

groups. The valid range of dates is October 15, 1582 to December 31, 9999. Default is mm.ddyyyy format.

Pressing

Note that when a date is displayed, a number between 1 and 7 also displays at the right of the screen. This number indicates the day of the week corresponding to that date. Monday is 1, and Sunday is 7.

NOTE: in 360-day calendar mode (Cal.360), days of the week are displayed only if the date is valid.

Default is decimal point, 1.23 .

: and release it. Check that the secondary function indicator is displayed.

corresponds to the desired FIX setting. FIX settings for 10 and 11 are not available using

this shortcut. If you press

. instead of a numbered key, FIX= –1 is selected.

I toggles between these options.

Pressing

1000.00, 1,000.00, 1000,00 or 1.000,00

Chain, Algebraic, or RPN Calculation mode. For more information, refer to Chapter 2, Mathematical Calculations.

English, Français, Deutch, or Español

Selects thousands separator. Default is none, 1000 .00

Pressing I toggles between these options.

NOTE: the 1000.00 and 1,000.00 options are only available if the decimal separator is set for point (.); 1000,00 and 1.000,00 are available only if the decimal separator is set for comma (,).

Pressing

Language setting for the messages displayed on the screen. Default is English.

Pressing

I toggles between these options.

I cycles through these options.

Basic Features

Table 1-1 Mode Menu Settings

Setting (top line) Description

Actual or Cal.360 Calendar options for bonds and date calculations.

Default is Actual.

Pressing I toggles between these options.

Annual or Semiannual Bond type.

Default is Annual.

I toggles between these options.

TVM Standard or TVM Canada

Pressing

Activate or deactivate the compounding per year (C/YR) option in time value of money (TVM) calculations. This option is primarily used for Canadian mortgage calculations. See Chapter 4, Canadian Mortgages: TVM Canada for more information.

Pressing

Changing the Calculation Mode

After viewing the default settings, suppose you want to change the calculation mode from

Chain to RPN. See Table 1-2.

Table 1-2 Changing the Calculation Mode

Keys Display Description

<<<

Opens the Mode menu, starting with first setting option, FIX, the number of digits displayed to the right of the decimal point.

Scrolls to the current setting for the calculation mode, Chain.

(Press five times)

(Press two times)

Key Presses, the Shift Key, Secondary, and Tertiary Functions*

To execute the function associated with a key, press and release the desired key. However, most of the calculators’ keys have more than one function: the first, or primary function, the shifted, or secondary function, and, in some cases, a third, or tertiary function (see Figure 2).

* Tertiary functions do not apply to the HP 20b.

Selects RPN as the active setting. Note the RPN annunciator to the right.

Exits the Mode menu and returns you to the default calculator screen.

Basic Features4

• The primary function is printed on the top of the key.

Primary Function

Shifted (secondary) Function

Black S Tertiary function: (press SHIFT and the function key simultaneously)

• The secondary function is printed on the bevel of the key. To activate the secondary function of a key,

press and release

• The third, or tertiary functions are printed above specific keys on the keyboard. To activate the

tertiary function of a key, press and hold function. Release both keys.

In this manual, key symbols of the commands are provided throughout the manual so you can follow along with the examples.

• The primary functions are represented by the key symbol with the primary function.

: followed by the key with the secondary function printed on the bevel.

: and simultaneously press the key below the printed

Figure 2 Primary, Secondary, and Tertiary Key Functions

When : is active, the down arrow annunciator appears on screen, indicating that the

next key pressed will execute the secondary function of the key. To cancel an accidental press

of :, simply press : a second time.

Key commands for example problems are provided throughout the text and in tables. Key symbols are placed in the order they are to be pressed, from left to right.

* Does not apply to the HP 20b.

• The secondary key functions are represented by the shift key symbol,

with the secondary function. For example, to execute sine, press

portion of the key is highlighted, while the of the key that will be activated in a given command.

• Commands with a tertiary function are represented by the shift key symbol, term (HOLD), followed by the key with the tertiary function. For example, to activate the Black-Scholes

feature shown above, press

:(HOLD) B*.

7 is grayed out. This highlighting focuses on the function

:, followed by the key

:p. Note how the SIN

:, followed by the

Basic Features

Annunciators

Valid item for the

Input

key

Secondary

function active

Valid item for

the Equals

key

RPN mode

active

Number recall

active

Low batteries

Radians active

Begin mode

active

Number storage

active

360 day-count calendar active

Assigned value

Annunciators are symbols that appear in the display as messages, or after certain keys or key combinations have been pressed. Annunciators are special symbols indicating a specific status in the calculator. Figure 3 illustrates the annunciator symbols in the display.

Figure 3 Annunciator Symbols in the Screen Display

The Input Key

The I key is used to input values for variables and execute menu items. The I key is also used in Reverse Polish Notation (RPN) mode to enter a number on

the stack or duplicate it.

The Equals Key

The = key is used at the end of a mathematical operation to calculate the final result. For example, 1+2= returns a final result of 3.

The

= key, when pressed outside of a mathematical operation, also allows you to request

a calculation for the value of an item. This request only applies to items that can be calculated.

Using the Input and Equals Keys

Suppose you wanted to calculate the effective interest rate for a 12% nominal interest rate with 12 payments per year in the Interest Conversion (IConv) menu. To open the IConv menu, press

:&. Nom %= displays on the top line, and the current value assigned to the nominal

Basic Features6

interest rate is displayed on the bottom line. With this screen displayed, press

12I to input a new value for the nominal rate. Press < followed by = to calculate the value for the effective rate. See Figure 4.

Figure 4

When an item for which the = key is valid displays, the small annunciator (=) is displayed

on the top line at the right of the screen. Do not confuse this small annunciator (=) with the larger annunciator (

When an item for which the I key is valid displays, the INPUT annunciator is

displayed on the top line at the right of the screen.

Editing and Clearing Entries The On/CE Key

) found to the right of a variable.

Pressing O one time cancels current number entries, mathematical operations, or a menu

selection, in that order.

Pressing O repeatedly when performing multiple operations cancels one operation at a

time, from the latest to the earliest.

The Reset Menu

The Reset menu allows you to reset some, or all, of the menu items, variables, and registers to their default values.

To open the Reset menu, press :x. TVM displays on the top line. Press < or >

repeatedly to scroll to a specific item. To validate a choice and reset the selected items, press

I. Press O to cancel. If you select the command to reset the cash flow (Cash Flow),

statistics (Stats ), programs (Prgm)* or all values (All ) items, you will be prompted to confirm your choice. At the Del. All?, Del. Data?, Del. Prgm?*, and Del. CF? prompts, press

again to confirm the reset, or

O to cancel. While working within a specific menu, pressing

:x takes you directly to the item of the Reset menu that allows you to reset that specific

menu. For example, if you are working in the Bond menu and you wish to reset all your entries in the Bond menu, with any item of the Bond menu displayed, press

on screen. At this prompt, pressing item you were working with in the Bond menu.

* Only applies to the HP 30b.

I resets the Bond menu and returns you to the last

:x. Bond displays

Basic Features

Notes about Special Menus

The Mode, Memory, Math and Reset menus are unique menus; they allow you to work in another menu simultaneously without having to exit. For example, if you were working in the

Bond menu prior to entering one of these menus, pressing O to exit returns you to your

previous work in the Bond menu.

Memory and the Memory Menu

The Memory menu contains the following items: memories 1–9 (Mem 1–9) and 0 (Mem 0), Cash Flow, Statistics (Stats), programs (Prgm)*, and Memory. To enter the menu, press

:t. Press < or > repeatedly to scroll through the items starting with

memory 1 (Mem 1).

When a memory item is displayed, you can key in a new number and modify the value of the memory by pressing

For more information about storing and recalling numbers, refer to the section titled, Storing and Recalling Numbers in Chapter 2.

The Cash Flow and Statistics data share the same memory and are limited to a combined total of 50 memory slots. The number displayed with Memory refers to the number of remaining memory slots. When the cash flow or statistics items are displayed, a number also appears on the bottom line. This number indicates the number of memory slots used by the cash flow or statistical data.

290 bytes are available for programs. The Prgm* menu item displays the number of bytes used.

Press I on the Cash Flow, Statistic, or Prgm* menu item to erase the associated data.

Since entering data in these menus can represent a significant amount of work, you will be asked to confirm your choice. At the Del.Data?, Del. Prgm?*, or Del.CF? prompts, press

I to confirm, or O to cancel.

Accessing Menus and Menu Maps

Many of the calculator's functions are located within menus. To access a menu, press the key, or secondary-function, key combination for the menu in which you wish to work. To exit a

menu, press

For example, to access the Break-even menu, press : .

* Only applies to the HP 30b.

Basic Features8

Once opened, you can scroll through the items in the menu by pressing < or > repeatedly. In most menus, when you arrive at the last item in a menu, pressing < returns you to the first item. Similarly, pressing > once on the first menu item scrolls to the last

item in the menu. Most items consist of two parts: a name and an associated number. For example, the Fixed

item in the Break-even menu (Figure 7) is displayed in Figure 5.

Figure 5

The large (=) annunciator shows that the value assigned to Fixed is 120,000. For example, if you perform a calculation with the operating mode set to RPN with this item displayed by

pressing 1I2+, Fixed is still selected as the current item, but the large

(=) annunciator is now turned off, indicating that the 3 is not the value assigned to Fixed (see Figure 6).

Figure 6

At this point, to return to the display of the Fixed menu item shown in Figure 5, press O.

Some menus have sub-menus. If an item represents a sub-menu, pressing I with that

menu item displayed opens the sub-menu. Once the menu sub-menu is open, use

> and

< to navigate through the items of the sub-menu, unless otherwise directed.

In this manual, diagrams called Menu Maps are included at the beginning of each section to assist you with navigating through the menus described in that section. For an example of a

menu map, see Figure 7 below. Once opened, use the through the menu items of the Break-even menu. The downward arrows in the map indicate

you press a sub-menu, the word INPUT appears in the arrow(s). For examples of menu maps with sub-

menus, see chapters 10-12. The return arrows direct you to the next item displayed after the

< to scroll to the next item. If a press of the I key is required to open

> and < keys to navigate

last item in a menu. For example, in Figure 7, pressing returns you to the FIXED item.

< on the last item in the menu

Basic Features

There are four types of menu items:

Fixed

DWN

Cost

Price

Profit

Quantity

1. Read/write. Read/write menu items, such as Fixed in the Break-even menu shown

2. Read-only. Read-only items such as Internal Rate of Return (IRR% ) in the IRR menu are

3. Write-only. Write-only items, such as investment interest rate (Inv. I% ) in the Net Present

Figure 7 Menu Map of the Break-even menu

above, are easily recognizable, because when they are selected, both the INPUT and small (=) annunciators are lit. When lit, these annunciators indicate that keying in a

number and pressing I will store the entered number in the displayed menu item. Pressing = (outside of a mathematical operation) calculates the value for that

item based on available data.

display-only; they are values computed internally by the calculator.

Value (NPV) menu, are similar to read/write items in that the INPUT annunciator is lit when these items are selected, indicating that keying in a number and pressing

I stores that number in that menu item. However, the = key does not

calculate a value for that item.

Basic Features10

4. Special items. Special items, such as the Degree/Radian option in the Mode menu, the items of the Reset menu, and the items of the Percent Calculation (%calc ) menu perform

an action when I is pressed. Depending on the menu, this action can be the

selection of a sub-menu (%calc), changing a mode or setting (Mode menu), or erasing data (Reset menu)

2 Mathematical Calculations

Mathematical Functions

Mathematical functions are located:

• On keys, such as, +-*/, etc.

• On shifted, or secondary functions, such as,

• In the Math menu, :s

Number Entry and Display

Numbers are entered by pressing:

• Numbered keys, 0–9

• The decimal point .

•The } key

•The

To correct a number entry, press the backspace key, {. Each press of { erases the last

digit or symbol you entered. To enter a number in the display, press the number digits successively. A number can have up

to 12 digits.

:w keys

To change the sign of a number from positive to negative, press }.

Use scientific notation to enter very large and very small numbers. For example, to enter the number 1.23x 10

127

in scientific notation, first enter the mantissa (1.2 3) and then press

:w and enter the number (127 ) representing the exponent. The exponent must have a

value between –499 and +499. If an expression has more than 12 digits, or if an operation returns a result with more than 12 digits, the calculator automatically displays scientific notation.

Figure 1 Scientific Notation in FIX=2 Mode

Mathematical Calculations

Chain Mode

Calculations in Chain mode are interpreted in the order in which they are entered. For example, entering the following numbers and operations as written from left to right,

1+2*3=, returns 9. See Figure 2.

Figure 2 Calculation in Chain Mode

NOTE: if you press an operator key, +-*/, after =, the calculation is

continued using the currently displayed value.

In Chain mode, if you wish to override the left to right order of entry, use parentheses

(D to prioritize operations.

For example, to calculate 1 + (2 x 3), you may enter the problem as written from left to right, with parentheses to prioritize the multiplication operation. See Table 2-1 below.

Table 2-1 Simple Arithmetic Calculations in Chain Mode

Keys Display Description

Sets operational priority, inputs numbers,

and multiplies 2 and 3.

(2*3D

Adds 1 to 6 and returns 7.0 0 on the bottom

Algebraic Mode

To set the calculator in Algebraic mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1.

In Algebraic mode, multiplication and division have a higher priority than addition and subtraction. For example, in Algebraic mode, pressing

returns a result of 7.0 0. In Chain mode, the same key presses return a result of 9.00.

line as the final result.

1+2*3=

In Algebraic mode, operations between two numbers have the following priority:

• Highest priority: the power function ( y x )

• Second priority: combinations and permutations

• Third priority: multiplication and division

• Lowest priority: addition and subtraction

Mathematical Calculations12

For example, key in 1 + 2 x 5 nPr 22 in Algebraic mode by pressing:

Stack Level 4

Stack Level 1

Stack Level 3

-15

Stack Level 2 41

1+2*5:b2:m=. The result is 241.

NOTE: the calculator is limited to 12 pending operations. An operation is pending when it is waiting for the input of a number or the result of an operation of higher priority.

Reverse Polish Notation (RPN) Mode

To set the calculator in RPN mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. In RPN mode, numbers are keyed in first, separated by pressing

I or =, followed by an operation key.

NOTE: pressing I or = is optional after keying in a number, if the next key

pressed is an operation. Each time you press an operation or function key in RPN, the answer is calculated immediately

and displayed. For example, suppose you wanted to add two numbers in RPN, 1 and 2. Press

1I2+. The result, 3.00, is calculated and displayed immediately on the

bottom line along with the (+) symbol on the top line.

The RPN Stack

NOTE: in RPN mode, when you are in a menu for which I or = are valid,

pressing these keys enters the number, but it also performs the action associated with the key for the menu item, which is generally saving the number in the variable or calculating the item's value.

RPN works by placing numbers in storage registers called the stack. The RPN stack has four levels numbered 1– 4. The levels are stacked on top of one another. See Figure 3.

Figure 3 The RPN Stack

Mathematical Calculations

In Figure 3, the stack contains four numbers, 23, 41, 12, and –15. Each level (1– 4) contains

-15

1.23 56.123+()

56.123()

--------------------------------------

one number. When a number is typed and entered into the stack by pressing I, this

new number is "pushed" into level one of the stack, and each number already in the stack moves up one level. The number in Level 4, –15, is pushed out and is lost.

When an operation is performed on the stack, addition "pops" or moves the two numbers from the bottom levels (Levels 1 and 2) out of the stack,

performs the operation, and "pushes" the results back into the stack.

With the numbers entered into the stack as shown in Figure 3, pressing stack as shown in Figure 4. Note that when the numbers are "popped" out to add 23 and 41,

Level 4 of the stack remains unchanged.

(+) for instance, the calculator

+ changes the

Last Number

Each time you perform a mathematical operation, the content of Level 1 of the stack is saved. Pressing

key press, or if you want to reuse a number, such as 56.123 in the expression:

See Table 2-2 for an example using the last number function.

Mathematical Calculations14

:d recalls that number. This functionality can be used to undo an erroneous

Figure 4 The RPN Stack of Figure 3 Shown After the Addition Operation

Table 2-2 Last Number

Keys Display Description

Sets FIX= to 3.000

:u3I

Selects RPN as the operating mode.

<<<< < II

Inputs 1.23 and 56.123

O1c23 I56c

1 23

Adds 1.23 and 56.123, then divides

+:d/

the sum by the last number, 56.123. Returns results in the selected display format.

For more complex problems requiring two or more operations, you do not need to enter parentheses to set operational priority. Key in numbers and operations inside the parentheses first, followed by those outside of the parentheses. If a problem has more than one set of parentheses, start by working with the operations and numbers in the innermost parentheses and work out. For example, calculate:

(3 + 4) x (5 + 6)

One way to calculate this problem is to key in the numbers and operations within the parentheses first, followed by the operation outside of the parentheses. See Table 2-3.

Mathematical Calculations

Table 2-3 Simple Arithmetic Calculations in RPN Mode

Value

Keys Display Description RPN Stack

Inputs the numbers and the

3I4

5I6

operation in the first set of parentheses. Intermediate results are displayed. Note the (+) and (RPN) annunciators.

Inputs the numbers and the operation in the second set of parentheses. Intermediate results are displayed. Note the (+) annunciator.

Finishes the operation and

displays the results.

Pressing I or = when you are not entering a number duplicates the number on

Level 1. That is, the number on Level 1 is pushed on the stack, making Levels 1 and 2 equal. In the example above, pressing

I after * duplicates 77 on the stack, making

Levels 1 and 2 equal. See Figure 5.

Mathematical Calculations16

Figure 5 Duplicating a Number on the Stack

Previous Value

-15

In RPN, the parentheses keys (D manipulate the stack. Pressing ( performs a roll

down of the stack. A roll down causes the stack to roll towards the bottom of the stack, during

which the number in Level 2 to moves down to Level 1, the number in Level 3 to moves down to Level 2, the number in Level 4 to moves down to Level 3, and the number of Level 1 to moves

up to Level 4. The ( key has a small down arrow on it to indicate the roll down feature. With the numbers entered into the stack shown in the left column in Figure 6, pressing (

performs the roll down of the stack shown in the right column.

Figure 6 The RPN Stack and the Roll Down Operation

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Pressing D performs a swap. A swap operation exchanges the numbers on Levels 1 and 2

-15

of the stack. The

D key has a small symbol to the right of the parenthesis symbol to indicate

the swap feature. With the numbers entered into the stack shown in the left column in Figure 7,

pressing D performs a swap to the stack as shown in the right column.

Figure 7 The RPN Stack and the Swap Operation

NOTE: when no menu is selected, the < key performs the same function as the ( key. The > key performs the inverse operation called, roll up.

One-Number Functions and the Math Menu

The key presses for the one-number mathematical functions listed in Table 2-4 below apply to all modes, Chain, Algebraic, and RPN. To execute one-number functions, with a number displayed, press the key or key combination corresponding to the operation you wish to execute. The result is displayed on the bottom line.

For example, to calculate , press 6:n. The result of 2.45 is calculated

immediately and displayed on the bottom line. Note the square root symbol appears on the top line.

NOTE: before doing any trigonometric calculations in the Math menu, check whether the angle mode is set for degrees (Degree) or radians (Radian). You will need to change the setting if the active mode is not what your problem requires. For more information on the Mode menu and calculator settings, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. Table 2-4 lists one-number functions along with their corresponding keys.

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Table 2-4 Shifted Function Mathematical Operations

Keys Description

:p :q :r :k :l :m :n :f :g

Calculates sine.

Calculates cosine.

Calculates tangent.

Calculates natural log.

Calculates natural exponent to the power of x.

Calculates square of x.

Calculates square root.

Executes the Random function. Returns a random number in the range 0 < x <1.

Calculates factorial of x (where –253 < x calculate x! for non-integers or negative numbers.

Calculates the reciprocal.

253). The Gamma function is used to

:d :e

In Chain or Algebraic mode, recalls the result of the last operation. In RPN mode, returns the content of the Last Number variable.

Rounds x to the number specified by the display format.

Random number

Press :f to generate a randomly distributed number between 0 and 1.

Type a number and press generation.

:$:f to store a new seed for random number

The Math Menu

There are additional functions available in the Math menu. To open the Math menu, press

:s. See Figure 8 for the menu map of the Math menu.

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DWN

INPUT

Trigonometry

Hyperbolic

Probability

ABS

(Absolute

Value)

SIN

-1

SINH

COSH

TANH

LTND

-1

LOG

INPUT

DWN

COS

-1

DWN

TAN

-1

TANH

-1

SINH

-1

COSH

-1

DWN

INPUT

DWN

Student

-1

Chi

2-1

F—Distribution

F-1—Distribution

DWN

Binomial

DWN

Press < to scroll through the menu items, starting with Trigonometry. The Trigonometry,

Figure 8 The Menu Map for the Math Menu

Hyperbolic, and Probability items have sub-menus. Press

access the functions within the sub menus. Press < to scroll through the functions.

* IP and FP functions are not available on the HP 20b.

I on any of these items to

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Press O to cancel the Math menu and return to current work. Press :s to return

to the top of the Math menu.

–1

For example, using the math menu calculate Sin

Table 2-5 Math Menu Example

Keys Display Description

.5I

(0.5), see Table 2-5.

Enters 0.5 and opens the Math menu starting with Trigonometry.

Selects the Trigonometry sub-menu and scrolls to

-1

. Note the value for Sin-1 is calculated

Sin

immediately and displayed.

Validates the result.

I or =

In the Math menu, PI does not perform calculations; it enters PI for calculations. You may start an operation, use the Math menu to execute a function, and continue calculating with your original operation without losing your work.

The Probability Sub-menu

Lower Tail Normal Distribution (LTND) calculates the probability for a normally distributed, random variable to be less than the input.

Inverse Lower Tail Normal Distribution (LTND-1) is the inverse function for LTND; it calculates the value (V) for which the probability of a normally distributed, random variable to be less

than V is the given input. Student, Inverse Student, Chi2 (2), Inverse Chi2, F-Distribution and Inverse F-Distribution perform similar operations for Student, Chi2, and F-Distributions.

Student, Chi require more than one number as input. Student and Chi2 require (N), the number of degrees

of freedom, and F-Distribution requires (N1) and (N2), two degrees of freedom. To perform Student and Chi

1. Enter the number of degree(s) of freedom by typing the number and pressing I or =.

2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which you want the number.

3. Navigate to the appropriate function in the Probability sub-menu of the Math menu.

, and F-Distribution and their inverse operations are special cases, as they

operations or their inverse:

To perform F-Distribution operations or their inverse:

Mathematical Calculations

1. Enter the two degrees of freedom by typing each number followed by I or

2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which you want the number.

3. Navigate to the appropriate function in the Probability sub-menu of the Math menu. See Table 2-6. Note: the examples below are calculated with Chain set as the operating mode.

Table 2-6 Probability Example

Keys Display Description

Enters 10 degrees of freedom and the number

10I 8I :s

<<I <<<<

for which probability is to be calculated. Opens the Math menu.

Selects the Probability menu item and scrolls to Chi2..

Validates the result.

I or =

Table 2-7 Inverse Probability Example

Keys Display Description

Enters 10 degrees of freedom and the

10I

probability. Opens the Math menu.

0.37

12I :s

Selects the Probability menu item. Scrolls to

<<I

Chi

2-1

<<<< <

I or =

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Validates the result.

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