HP 15c User Manual

HP-15C

Owner’s Handbook

HP Part Number: 00015-90001

Edition 2.4, Sep 2011

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 incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein.

Copyright © 2011 Hewlett-Packard Development Company, LP.

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 Palo Alto, CA

94304 USA

Introduction

Congratulations! Whether you are new to HP calculators or an experienced user, you will find the HP-15C a powerful and valuable calculating tool. The HP-15C provides:

448 bytes of program memory (one or two bytes per instruction) and sophisticated programming capability, including conditional and unconditional branching, subroutines, flags, and editing.

Four advanced mathematics capabilities: complex number calculations, matrix calculations, solving for roots, and numerical integration.

Direct and indirect storage in up to 67 registers.

This handbook is written for you, regardless of your level of expertise. The beginning part covers all the basic functions of the HP-15C and how to use them. The second part covers programming and is broken down into three subsections – The Mechanics, Examples, and Further Information – in order to make it easy for users with varying backgrounds to find the information they need. The last part describes the four advanced mathematics capabilities.

Before starting these sections, you may want to gain some operating and programming experience on the HP-15C by working through the introductory material, The HP-15C: A Problem Solver, on page 12.

The various appendices describe additional details of calculator operation, as well as warranty and service information. The Function Summary and Index and the Programming Summary and Index at the back of this manual can be used for quick reference to each function key and as a handy page reference to more comprehensive information inside the manual.

Also available from Hewlett-Packard is the HP-15C Advanced Functions Handbook, which provides applications and technical descriptions for the root-solving, integration, complex number, and matrix functions.

Note: You certainly do not need to read every part of the manual before delving into the HP-15C Advanced Functions if you are already familiar with HP calculators. The use of _ and f requires a knowledge of HP-15C programming.

3

Contents

The HP-15C: A Problem Solver ....................................	12
A Quick Look at v .................................................	12
Manual Solutions ............................................................	13
Programmed Solutions .....................................................	14

Part I: HP-15C Fundamentals ................................	17
Section 1: Getting Started ..........................................	18
Power On and Off ..........................................................	18
Keyboard Operation .......................................................	18
Primary and Alternate Functions .....................................	18
Prefix Keys ..................................................................	19
Changing Signs ...........................................................	19
Keying in Exponents .....................................................	19
The "CLEAR" Keys ........................................................	20
Display Clearing: `and − ...................................	21
Calculations ...................................................................	22
One-Number Functions .................................................	22
Two-Number Functions and v ...............................	22
Section 2: Numeric Functions .....................................	24
Pi ..................................................................................	24
Number Alteration Functions ............................................	24
One-Number Functions ....................................................	25
General Functions ........................................................	25
Trigonometric Operations ..............................................	26
Time and Angle Conversions .........................................	26
Degrees/Radians Conversions .......................................	27
Logarithmic Functions ...................................................	28
Hyperbolic Functions ....................................................	28
Two-Number Functions ....................................................	29
The Power Function ......................................................	29
Percentages .................................................................	29
Polar and Rectangular Coordinate Conversions ...............	30
Section 3: The Automatic Memory Stack, LAST X, and
Data Storage ........................................................	32
4

Contents	5
The Automatic Memory Stack and Stack Manipulation ........	32
Stack Manipulation Functions ........................................	33
The LAST X Register and K .......................................	35
Calculator Functions and the Stack .................................	36
Order of Entry and the v Key ...............................	37
Nested Calculations .....................................................	38
Arithmetic Calculations With Constants ...........................	39
Storage Register Operations ............................................	42
Storing and Recalling Numbers .....................................	42
Clearing Data Storage Registers ....................................	43
Storage and Recall Arithmetic ........................................	43
Overflow and Underflow ..............................................	45
Problems ........................................................................	45
Section 4: Statistics Functions .....................................	47
Probability Calculations ...................................................	47
Random Number Generator .............................................	48
Accumulating Statistics .....................................................	49
Correcting Accumulated Statistics ...................................	52
Mean ..........................................................................	53
Standard Deviation .......................................................	53
Linear Regression .........................................................	54
Linear Estimation and Correlation Coefficient ...................	55
Other Applications .......................................................	57
Section 5: The Display and Continuous Memory ...........	58
Display Control ..............................................................	58
Fixed Decimal Display ..................................................	58
Scientific Notation Display ............................................	59
Engineering Notation Display ........................................	59
Mantissa Display .........................................................	60
Round-Off Error ............................................................	60
Special Displays .............................................................	60
Annunciators ...............................................................	60
Digit Separators ...........................................................	61
Error Display ...............................................................	61
Overflow and Underflow ..............................................	61
Low-Power Indication ....................................................	62
Continuous Memory ........................................................	62
Status .........................................................................	62

6	Contents
	Resetting Continuous Memory ........................................	63
Part II: HP-15C Programming ...............................		65
Section 6: Programming Basics ..................................		66
	The Mechanics ...............................................................	66
	Creating a Program .....................................................	66
	Loading a Program ......................................................	66
	Intermediate Program Stops ...........................................	68
	Running a Program .......................................................	68
	How to Enter Data ........................................................	69
	Program Memory .........................................................	70
	Further Information ..........................................................	74
	Program Instructions .....................................................	74
	Instruction Coding ........................................................	74
	Memory Configuration ..................................................	75
	Program Boundaries .....................................................	77
	Unexpected Program Stops ...........................................	78
	Abbreviated Key Sequences ..........................................	78
	User Mode ..................................................................	79
	Polynomial Expressions and Horner's Method ..................	79
	Nonprogrammable Functions .........................................	80
	Problems ........................................................................	81
Section 7: Program Editing ........................................		82
	The Mechanics ...............................................................	82
	Moving to a Line in Program Memory .............................	82
	Deleting Program Lines .................................................	83
	Inserting Program Lines .................................................	83
	Examples .......................................................................	83
	Further Information ..........................................................	85
	Single-Step Operations .................................................	85
	Line Position ................................................................	86
	Insertions and Deletions ................................................	87
	Initializing Calculator Status ..........................................	87
	Problems ........................................................................	87
Section 8: Program Branching and Controls .................		90
	The Mechanics ...............................................................	90
	Branching ...................................................................	90
	Conditional Tests ..........................................................	91

	Contents	7
Flags ..........................................................................	92
Examples .......................................................................	93
Example: Branching and Looping ...................................	93
Example: Flags ............................................................	95
Further Information ..........................................................	97
GoTo ..........................................................................	97
Looping ......................................................................	98
Conditional Branching ..................................................	98
Flags ..........................................................................	98
The System Flags: Flags 8 and 9 ....................................	99
Section 9: Subroutines ...............................................	101
The Mechanics ...............................................................	101
GoTo Subroutine and Return ..........................................	101
Subroutine Limits ..........................................................	102
Examples .......................................................................	102
Further Information ..........................................................	105
The Subroutine Return ...................................................	105
Nested Subroutines ......................................................	105
Section 10: The Index Register and Loop Control ...........	106
The V and % Keys ....................................................	106
Direct Versus Indirect Data Storage With
The Index Register .....................................................	106
Indirect Program Control With the Index Register .............	107
Program Loop Control ...................................................	107
The Mechanics ...............................................................	107
Index Register Storage and Recall ..................................	107
Index Register Arithmetic ...............................................	108
Exchanging the X-Register .............................................	108
Indirect Branching With V .........................................	108
Indirect Flag Control With V ......................................	109
Indirect Display Format Control With V .......................	109
Loop Control with Counters: Iand e ..................	109
Examples .......................................................................	111
Examples: Register Operations .......................................	111
Example: Loop Control With s .................................	112
Example: Display Format Control ....................................	114
Further Information ..........................................................	115
Index Register Contents .................................................	115

8	Contents
	Iand e ..........................................................	116
	Indirect Display Control ...........................................	116
Part III: HP-15C Advanced Functions ....................		119
Section 11: Calculating With Complex Numbers ..........		120
	The Complex Stack and Complex Mode ............................	120
	Creating the Complex Stack ..........................................	120
	Deactivating Complex Mode .........................................	121
	Complex Numbers and the Stack ......................................	121
	Entering Complex Numbers ...........................................	121
	Stack Lift in Complex Mode ...........................................	124
	Manipulating the Real and Imaginary Stacks ..................	124
	Changing Signs ..........................................................	124
	Clearing a Complex Number .......................................	125
	Entering a Real Number ...............................................	128
	Entering a Pure Imaginary Number ...............................	129
	Storing and Recalling Complex Numbers .......................	130
	Operations With Complex Numbers ................................	130
	One-Number Functions ................................................	131
	Two-Number Functions .................................................	131
	Stack Manipulation Functions .......................................	131
	Conditional Tests .........................................................	132
	Complex Results from Real Numbers ..............................	133
	Polar and Rectangular Coordinate Conversions .................	133
	Problems .......................................................................	135
	For Further Information ...................................................	137
Section 12: Calculating With Matrices ........................		138
	Matrix Dimensions .........................................................	140
	Dimensioning a Matrix .................................................	141
	Displaying Matrix Dimensions .......................................	142
	Changing Matrix Dimensions ........................................	142
	Storing and Recalling Matrix Elements ..............................	143
	Storing and Recalling All Elements in Order ...................	143
	Checking and Changing Matrix Elements Individually .....	145
	Storing a Number in All Elements of a Matrix .................	147
	Matrix Operations .........................................................	147
	Matrix Descriptors .......................................................	147
	The Result Matrix .........................................................	148

	Contents	9
Copying a Matrix .......................................................	149
One-Matrix Operations ................................................	149
Scalar Operations .......................................................	151
Arithmetic Operations ..................................................	153
Matrix Multiplication ...................................................	154
Solving the Equation AX = B..........................................	156
Calculating the Residual ...............................................	159
Using Matrices in LU Form ............................................	160
Calculations With Complex Matrices ...............................	160
Storing the Elements of a Complex Matrix ......................	161
The Complex Transformations Between ZP and Z .............	164
Inverting a Complex Matrix ..........................................	165
Multiplying Complex Matrices ......................................	166
Solving the Complex Equation AX = B ............................	168
Miscellaneous Operations Involving Matrices .....................	173
Using a Matrix Element With Register Operations ............	173
Using Matrix Descriptors in the Index Register .................	173
Conditional Tests on Matrix Descriptors ..........................	174
Stack Operation for Matrix Calculations ............................	174
Using Matrix Operations in a Program ..............................	176
Summary of Matrix Functions ...........................................	177
For Further Information ....................................................	179
Section 13: Finding the Roots of an Equation ................	180
Using _ .................................................................	180
When No Root Is Found ..................................................	186
Choosing Initial Estimates ................................................	188
Using _ in a Program ..............................................	192
Restriction on the Use of _ .......................................	193
Memory Requirements .....................................................	193
For Further Information ....................................................	193
Section 14: Numerical Integration ..............................	194
Using f.......................................................................	194
Accuracy of f .............................................................	200
Using fin a Program ..................................................	203
Memory Requirements .....................................................	204
For Further Information ....................................................	204

10	Contents
Appendix A: Error Conditions ....................................		205
Appendix B: Stack Lift and the LAST X Register ...............		209
	Digit Entry Termination ....................................................	209
	Stack Lift ........................................................................	209
	Disabling Operations ...................................................	210
	Enabling Operations ....................................................	210
	Neutral Operations ......................................................	211
	LAST X Register ...............................................................	212
Appendix C: Memory Allocation ................................		213
	The Memory Space .........................................................	213
	Registers .....................................................................	213
	Memory Status (W) ..................................................	215
	Memory Reallocation ......................................................	215
	The m% Function ................................................	215
	Restrictions on Reallocation ...........................................	216
Program Memory ............................................................		217
	Automatic Program Memory Reallocation ........................	217
	Two-Byte Program Instructions .......................................	218
	Memory Requirements for the Advanced Functions .............	218
Appendix D: A Detailed Look at _ ......................		220
	How _Works .......................................................	220
	Accuracy of the Root .......................................................	222
	Interpreting Results ..........................................................	226
	Finding Several Roots ......................................................	233
	Limiting the Estimation Time ..............................................	238
	Counting Iterations .......................................................	239
	Specifying a Tolerance .................................................	239
	For Advanced Information ................................................	239
Appendix E: A Detailed Look at f ...........................		240
	How f Works .............................................................	240
	Accuracy, Uncertainty, and Calculation Time .....................	241
	Uncertainty and the Display Format ...................................	245
	Conditions That Could Cause Incorrect Results ....................	249
	Conditions That Prolong Calculation Time ..........................	254
	Obtaining the Current Approximation to an Integral ...........	257
	For Advanced Information ................................................	258

Contents	11
Appendix F: Batteries .............................................	259
Low-Power Indication .......................................................	259
Installing New Batteries ................................................	259
Verifying Proper Operation (Self-Tests) ...............................	261
Function Summary and Index .....................................	262
Complex Functions ..........................................................	262
Conversions ...................................................................	262
Digit Entry ......................................................................	262
Display Control ..............................................................	263
Hyperbolic Functions .......................................................	263
Index Register Control .....................................................	263
Logarithmic and Exponential Functions ..............................	263
Mathematics ..................................................................	264
Matrix Functions .............................................................	264
Number Alteration ..........................................................	265
Percentage .....................................................................	266
Prefix Keys .....................................................................	266
Probability .....................................................................	266
Stack Manipulation .........................................................	266
Statistics ........................................................................	267
Storage .........................................................................	267
Trigonometry ..................................................................	268
Programming Summary and Index ..............................	269
Subject Index ...........................................................	271

The HP-15C:

A Problem Solver

The HP-15C Advanced Programmable Scientific Calculator is a powerful problem solver, convenient to carry and easy to hold. Its continuous memory retains data and program instructions indefinitely until you choose to reset it. Though sophisticated, it requires no prior programming experience or knowledge of programming languages to use it.

The new HP-15C is a modern re-release of the original HP-15C introduced in 1982. While the battery life of the new version is now estimated to be 1 year for normal use, the calculator is now at least 150 times faster than the original. The low-power indicator gives you plenty of warning before the calculator stops functioning.

The HP-15C also conserves power by automatically shutting its display off if it is left inactive for a few minutes. But don't worry about losing data – any information contained in the HP-15C is saved by Continuous Memory.

A Quick Look at v

Your Hewlett-Packard calculator uses a unique operating logic, represented by the v key, that differs from the logic in most other calculators. You will find that using v makes nested and complicated calculations easier and faster to work out. Let's get acquainted with how this works.

For example, let's look at the arithmetic functions. First we have to get the numbers into the machine. Is your calculator on? If not, press =. Is the display cleared? To display all zeros, you can press | ` that is, press |, then −.* To perform arithmetic, key in the first number, press v to separate the first number from the second, then key in the second number and press +, -, *or ÷. The result appears immediately after you press any numerical function key.

*If you have not used an HP calculator before, you will notice that most keys have three labels. To use the primary function – the one printed in white on top of the key – just press that key. For those printed in gold or blue, press the gold ´key or the blue |key first.

12

The HP-15C: A Problem Solver 13

The display format used in this handbook is • 4 (the decimal point is

―fixed‖ to show four decimal places) unless otherwise mentioned. If your calculator does not show four decimal places, you may want to press ´•4 to match the displays in the examples.

Manual Solutions

Run through the following two-number calculations. It is not necessary to clear the calculator between problems. If you enter a digit incorrectly, press −to undo the mistake, then key in the correct number.

To Compute		Keystrokes	Display
9	- 6 = 3	9 v6 -	3.0000
9	× 6 = 54	9 v6 *	54.0000
9	÷ 6 = 1.5	9 v6 ÷	1.5000
96 = 531,441		9 v6 Y	531,441.0000

Notice that in the four examples:

Both numbers are in the calculator before you press the function key.

vis used only to separate two numbers that are keyed in one after the other.

Pressing a numeric function key, in this case -*÷or Y, executes the function immediately and displays the result.

To see the close relationship between manual and programmed problem solving, let's first calculate the solution to a problem manually, that is, from the keyboard. Then we'll use a program to calculate the solution to the same problem with different data.

14 The HP-15C: A Problem Solver

The time an object takes to fall to the ground (ignoring air friction) is given by the formula

t	2h	,
	g

where t = time in seconds, h = height in meters,

g = the acceleration due to gravity, 9.8 m/s2.

Example: Compute the time taken by a stone falling from the top of the Eiffel Tower (300.51 meters high) to the earth.

Keystrokes	Display
300.51 v	300.5100	Enter h.
2 *	601.0200	Calculates 2h.
9.8 ÷	61.3286	(2h) /g.
¤	7.8313	Falling time, seconds.

Programmed Solutions

Suppose you wanted to calculate falling times from various heights. The easiest way is to write a program to cover all the constant parts of a calculation and provide for entry of variable data.

Writing the Program. The program is similar to the keystroke sequence you used above. A label is useful to define the beginning of a program, and a return is useful to mark the end of a program. Also, the program must accommodate the entry of new data.

Loading the Program. You can load a program for the above problem by pressing the following keys in sequence. (The display shows information which you can ignore for now, though it will be useful later.)

		The HP-15C: A Problem Solver 15
Keystrokes	Display
|¥	000-		Sets HP-15C to Program
			mode. (PRGM
			annunciator on.)
´CLEAR M 000-			Clears program memory.
			(This step is optional
			here.)
´bA	001-42,21,11		Label "A" defines the
			beginning of the
			program.
2	002-	2
*	003-	20
9	004-	9
			The same keys you
			pressed to solve the
.	005-	48	problem manually.
8	006-	8
÷	007-	10
¤	008-	11
|n	009-	43 32	―Return‖ defines the end
			of the program.
|¥	7.8313		Switches to Run mode.
			(No PRGM
			annunciator.)

Running the Program. Enter the following information to run the program.

Keystrokes	Display
300.51	300.51	Height of the Eiffel Tower.
´A	7.8313	Falling time you calculated
		earlier.
1050 ´A	14.6385	The time (seconds) for a stone
		to reach the ground after release
		from a blimp 1050 m high.

16 The HP-15C: A Problem Solver

With this program loaded, you can quickly calculate the time of descent of an object from different heights. Simply key in the height and press ´A. Find the time of descent for objects released from heights of 100 m, 2 m, 275 m, and 2,000 m.

The answers are: 4.5175 s; 0.6389 s; 7.4915 s; and 20.2031 s.

That program was relatively easy. You will see many more aspects and details of programming in part II. For now, turn the page to take an in-depth look at some of the calculator's important operating basics.

Part l

HP-15C

Fundamentals

Section 1

Getting Started

Power On and Off

The = key turns the HP-15C on and off.* To conserve power, the calculator automatically turns itself off after a few minutes of inactivity.

Keyboard Operation

Primary and Alternate Functions

Most keys on your HP-15C perform one primary and two alternate, shifted functions. The primary function of any key is indicated by the character(s) on the face of the key. The alternate functions are indicated by the gold characters printed above the key and the blue characters printed on the lower face of the key.

To select the primary function printed on the face of a key, press only that key. For example: ÷.

To select the alternate function printed in gold or blue, press the like-colored prefix key (´or |) followed by the function key. For example: ´_; | £.

Throughout this handbook, we will observe certain conventions in referring to alternate functions. References to the function itself will appear as just the key name in a box, such as ―the W function.‖ References to the use of the key will include the prefix key, such as ―press | W.‖ References to the four gold functions printed under the bracket labeled ―CLEAR‖ will be preceded by the word ―CLEAR‖, such as "the CLEAR Q function,‖ or ―press ´CLEAR M.‖

* Note that the =key is lower than the other keys to help prevent its being pressed inadvertently.

18

Section 1: Getting Started		19
Notice that when you press the ´ or |
prefix key, an f or g annunciator appears	0.0000
and remains in the display until a function
	f

key is pressed to complete the sequence.

Prefix Keys

A prefix key is any key which must precede another key to complete the key sequence for a function. Certain functions require two parts: a prefix key and a digit or other key. For your reference, the prefix keys are:

"^ • G f > i O

m ´ | P I l F T s ? t H b < _ X

If you make a mistake while keying in a prefix for a function, press ´ CLEAR uto cancel the error. The CLEAR ukey is also used to show the mantissa of a displayed number, so all 10 digits of the number in the display will appear for a moment after the ukey is pressed.

Changing Signs

Pressing “(change sign) will change the sign (positive or negative) of any displayed number. To key in a negative number, press “ after its digits have been keyed in.

Keying in Exponents

‛(enter exponent) is used when keying in a number with an exponent. First key in the mantissa, then press ‛and key in the exponent.

For a negative exponent press “ after keying in the exponent.* For example, to key in Planck's constant (6.6262×10-34 Joule-seconds) and multiply it by 50:

*“may also be pressed after ‛and before the exponent, with the same result (unlike the mantissa, where digit entry must precede “).

20	Section 1: Getting Started
Keystrokes		Display
6.6262		6.6262
‛		6.6262	00	The 00 prompts you to
				key in the exponent.
3		6.6262	03	(6.6262×103).
4		6.6262	34	(6.6262×1034).
“		6.6262	-34	(6.6262×10-34).
v		6.6262	-34	Enters number.
50 *		3.3131	-32	Joule-seconds.

Note: Decimal digits from the mantissa that spill into the exponent field will disappear from the display when you press ―, but will be retained internally.

To prevent a misleading display pattern, ‛ will not operate with a number having more than seven digits to the left of the radix mark (decimal point), nor with a mantissa smaller than 0.000001. To key in such a number, use a form having a greater exponent value (whether positive or negative). For example, 123456789.8×1023 can be keyed in as 1234567.898×1025; 0.00000025×10-15 can be keyed in as 2.5×10-22.

The “CLEAR” Keys

Clearing means to replace a number with zero. The clearing operations in the HP-15C are (the table is continued on the next page):

Clearing Sequence	Effect
|`	Clears display (X-register).
−
In Run mode:	Clears last digit or entire display.
In Program mode:	Deletes current instruction.
´CLEAR ∑	Clears statistics storage registers, display,
	and the memory stack (described in
	section 3).

	Section 1: Getting Started 21
Clearing Sequence	Effect
´CLEAR M
In Run mode:	Repositions program memory to line 000.
In Program mode:	Deletes all program memory.
´CLEAR Q	Clears all data storage registers.
´CLEAR u*	Clears any prefix from a partially entered
	key sequence.

* Also temporarily displays the mantissa.

Display Clearing: `and −

The HP-15C has two types of display clearing operations: `(clear X) and −(back arrow).

In Run mode:

`clears the display to zero.

− deletes only the last digit in the display if digit entry has not been terminated by v or most other functions. You can then key in a new digit or digits to replace the one(s) deleted. If digit entry has been terminated, then −acts like `.

Keystrokes	Display
12345	12,345	Digit entry not terminated.
−	1,234	Clears only the last digit.
9	12,349

¤111.1261 Terminates digit entry.

−0.0000 Clears all digits to zero.

In Program mode:

` is programmable: it is stored as a programmed instruction, and will not delete the currently displayed instruction.

− is not programmable, so it can be used for program correction. Pressing −will delete the entire instruction currently displayed.

22 Section 1: Getting Started

Calculations

One-Number Functions

A one-number function performs an operation using only the number in the display. To use any one-number function, press the function key after the number has been placed in the display.

Keystrokes	Display
45	45
|o	1.6532

Two-Number Functions and v

A two-number function must have two numbers present in the calculator before executing the function. +, -, * and ÷ are examples of two-number functions.

Terminating Digit Entry. When keying in two numbers to perform an operation, the calculator needs a signal that digit entry is terminated for the first number. This is done by pressing vto separate the two numbers. If, on the other hand, one of the numbers is already in the calculator as the result of a previous operation, you do not need to use the v key. All functions except the digit entry keys themselves* have the effect of terminating digit entry.

Notice that, regardless of the number, a decimal point always appears and a set number of decimal places are displayed when you terminate digit entry (as by pressing v).

Chain Calculations. In the following calculations, notice that:

The v key is used only for separating the sequential entry of two numbers.

The operator is keyed in only after both operands are in the calculator.

The result of any operation may itself become an operand. Such intermediate results are stored and retrieved on a last-in, first-out basis. New digits keyed in following an operation are treated as a new number.

*The digit keys, +, “, ‛, and −.

		Section 1: Getting Started 23
Example: Calculate (9 + 17 4) ÷ 4.
Keystrokes	Display
9 v	9.0000	Digit entry terminated.
17 +	26.0000	(9 + 17).
4 -	22.0000	(9 + 17	– 4).
4 ÷	5.5000	(9 + 17	– 4) ÷ 4.

Even more complicated problems are solved in the same manner-using automatic storage and retrieval of intermediate results. It is easiest to work from the inside of parentheses outwards, just as you would with calculations on paper.

Example: Calculate (6 + 7) × (9 3)

Keystrokes	Display
6 v	6.0000
7 +	13.0000
9 v	9.0000
3 -	6.0000
*	78.0000

First solve for the intermediate result of (6 + 7).

Then solve for the intermediate result of (9 3).

Then multiply the intermediate results together (13 and 6) for the final answer.

Try your hand at the following problems. Each time you press vor a function key in a calculation, the preceding number is saved for the next operation.

(16 × 38) – (13 × 11) = 465.0000 4 × (17 – 12) ÷ (10 – 5) = 4.0000

232 – (13 × 9) + 1/7 = 412.1429

[(5.4 0.8) (12.5 0.72 )] 0.5998

Section 2

Numeric Functions

This section discusses the numeric functions of the HP-15C (excluding statistics and advanced functions). The nonnumeric functions are discussed separately (digit entry in section 1, stack manipulation in section 3, and display control in section 5).

The numeric functions of the HP-15C are used in the same way whether executed from the keyboard or in a program. Some of the functions (such as a) are, in fact, primarily of interest for programming.

Remember that the numeric functions, like all functions except digit entry functions, automatically terminate digit entry. This means a numeric function does not need to be preceded or followed by v.

Pi

Pressing | $ places the first 10 digits of π into the calculator. $ does not need to be separated from other numbers by v.

Number Alteration Functions

The number alteration functions act upon the number in the display (X-register).

Integer Portion. Pressing | ‘ replaces the number in the display with the nearest integer of lesser or equal magnitude.

Fractional Portion. Pressing ´qreplaces the number in the display with its fractional part (that is, the difference between the number and its integer part).

Rounding. Pressing | & rounds all 10 internally held digits of the mantissa of the displayed value to the number of digits specified by the current •, i, or ^display format.

Absolute Value. Pressing | a yields the absolute value of the number in the display.

24

	Section 2: Numeric Functions 25
Keystrokes	Display
123.4567 |‘	123.0000
|K“|‘ -123.0000		Reversing the sign does
		not alter digits.
|K´q	-0.4567
1.23456789 “
|&	-1.2346
´CLEAR u	1234600000	Temporarily displays all
(release)	-1.2346	digits in the mantissa.
|a	1.2346

One-Number Functions

One-number math functions in the HP-15C operate only upon the number in the display (X-register).

General Functions

Reciprocal. Pressing ∕ calculates the reciprocal of the number in the display.

Factorial and Gamma. Pressing ´ ! calculates the factorial of the displayed value, where x is an integer 0≤x≤69.

You can also use ! to calculate the Gamma function, Γ(x), used in advanced mathematics and statistics. Pressing ´!calculates Γ(x + 1), so you must subtract 1 from your initial operand to get Γ(x). For the Gamma function, x is not restricted to nonnegative integers.

Square Root. Pressing ¤ calculates the positive square root of the number in the display.

Squaring. Pressing | x calculates the square of the number in the display.

Keystrokes	Display
25 ∕	0.0400
8 ´!	40,320.0000	Calculates 8! or Γ(9).
3.9 ¤	1.9748
12.3 |x	151.2900

26 Section 2: Numeric Functions

Trigonometric Operations

Trigonometric Modes. The trigonometric functions operate in the trigonometric mode you select. Specifying a trigonometric mode does not convert any number already in the calculator to that mode; it merely tells the calculator what unit of measure (degrees, radians, or grads) to assign a number for a trigonometric function.

Pressing | D sets Degrees mode. No annunciator appears in the display. Degrees are in decimal, not minutes-seconds form.

Pressing | R sets Radians mode. The RAD annunciator appears in the display. In Complex mode, all functions (except : and ;) assume values are in radians, regardless of the trigonometric annunciator displayed.

Pressing | g sets Grads mode. The GRAD annunciator appears in the display.

Continuous Memory will maintain the last trigonometric mode selected. At "power up" (initial condition or when Continuous Memory is reset), the calculator is in Degrees mode,

Trigonometric Functions. Given x in the display (X-register):

Pressing	Calculates
[	sine of x
|,	arc sine of x
\	cosine of x
|{	arc cosine of x
]	tangent of x
|/	arc tangent of x

Before executing a trigonometric function, be sure that the calculator is set to the desired trigonometric mode (Degrees, Radians, or Grads).

Time and Angle Conversions

Numbers representing time (hours) or angles (degrees) can be converted by the HP-15C between a decimal-fraction and a minutes-seconds format:

	Section 2: Numeric Functions	27
Hours.Decimal Hours	Hours.Minutes Seconds Decimal Seconds
(H.h)	(H.MMSSs)
Degrees.Decimal Hours	Degrees.Minutes Seconds Decimal Seconds
(D.d)	(D.MMSSs)

Hours/Degrees-Minutes-Seconds Conversion. Pressing ´ h converts the number in the display from a decimal hours/degrees format to an hours/degree-minutes-seconds-decimal seconds format.

For example, press ´hto convert

1.2 3 4 5		1 . 1 4 0 4
	to	seconds
		minutes
hours		hours

Press ´uto display the value to all possible decimal places:

1 1 4 0 4 2 0 0 0 0

to the hundred-thousandth of a second.

Decimal Hours (or Degrees) Conversion. Pressing | À converts the number in the display from an hours/degrees-minutes-seconds-decimal seconds format to a decimal hours/degrees format.

Degrees/Radians Conversions

The d and r functions are used to convert angles to degrees or radians (D.d R.r). The degrees must be expressed as decimal numbers, and not in a minutes-seconds format.

Keystrokes	Display
40.5 ´r	0.7069	Radians.
|d	40.5000	40.5 degrees (decimal fraction).

28 Section 2: Numeric Functions

Logarithmic Functions

Natural Logarithm. Pressing |Z calculates the natural logarithm of the number in the display; that is, the logarithm to the base e.

Natural Antilogarithm. Pressing ' calculates the natural antilogarithm of the number in the display; that is, raises e to the power of that number.

Common Logarithm. Pressing | o calculates the common logarithm of the number in the display; that is, the logarithm to the base 10.

Common Antilogarithm. Pressing @ calculates the common antilogarithm of the number in the display; that is, raises 10 to the power of that number.

Keystrokes		Display
45 |Z		3.8067
3.4012	'	30.0001
12.4578 |o		1.0954
3.1354	@	1,365.8405

Hyperbolic Functions

Given x in the display (X-register):

Natural log of 45. Natural antilog of 3.4012. Common log of 12.4578.

Common antilog of 3.1354.

Pressing	Calculates
´P[	hyperbolic sine of x
|H[	inverse hyperbolic sine of x
´P\	hyperbolic cosine of x
|H\	inverse hyperbolic cosine of x
´P]	hyperbolic tangent of x
|H]	inverse hyperbolic tangent of x

Section 2: Numeric Functions

29

Two-Number Functions

The HP-15C performs two-number math functions using two values entered sequentially into the display. If you are keying in both numbers, remember that they must be separated by v or any other function – like | ‘or ∕– that terminates digit entry.

For a two-number function, the first value entered is considered the y-value because it is placed into the Y-register for memory storage. The second value entered is considered the x-value because it remains in the display, which is the X-register.

The arithmetic operators, +, -, *, and ÷, are the four basic twonumber functions. Others are given below.

The Power Function

Pressing Y calculates the value of y raised to the x power. The base number, y, is keyed in before the exponent, x.

To Calculate					Keystrokes		Display
21.4					2 v1.4	Y	2.6390
2-1.4					2 v1.4	“Y	0.3789
(-2)3					2 “v3 Y		-8.0000
3			or 2	1/3	2 v3 ∕Y		1.2599
	2

Percentages

The percentage functions, k and ∆, preserve the value of the original base number along with the result of the percentage calculation. As shown in the example below, this allows you to carry out subsequent calculations using the base number and the result without re-entering the base number.

Percent. The k function calculates the specified percentage of a base number.

30 Section 2: Numeric Functions

For example, to find the sales tax at 3% and total cost of a $15.76 item:

Keystrokes	Display
15.76 v	15.7600	Enters the base number (the price).
3 |k	0.4728	Calculates 3% of $15.76 (the tax).

+16.2328 Total cost of item ($15.76 + $0.47).

Percent Difference. The ∆ function calculates the percent difference between two numbers. The result expresses the relative increase (a positive result) or decrease (a negative result) of the second number entered compared to the first number entered.

For example, suppose the $15.76 item only cost $14.12 last year. What is the percent difference in last year’s price relative to this year’s?

Keystrokes	Display
15.76 v	15.7600	This year's price (our base number)
14.12 |∆	-10.4061	Last year's price was 10.41% less
		than this year's price.

Polar and Rectangular Coordinate Conversions

The :and ;functions are provided in the HP-15C for conversions between polar coordinates and rectangular coordinates. The angle θ is assumed to be in the mode, whether degrees (in a decimal format, not a minutesseconds format), radians, or grads. θ is measured as shown in the illustration at right.

Polar Conversion. Pressing |:

(polar) converts a set of rectangular coordinates (x, y) to polar coordinates (magnitude r, angle θ). The y-value must be entered first, the x-value second. Upon executing |: r will appear in the display. Press ® (X exchange Y) to bring θ out of the Y-register and into the display (X- register). θ will be returned as a value between -180° and 180°, between -π and π radians, or between -200 and 200 grads.