HP 15C User guide

OWNER’S HANDBOOK
HP 15c Collector’s Edition
SCIENTIFIC CALCULATOR


HP 15c Collector’s Edition
Owner’s Handbook
Edition 3, February 2023

Acknowledgements
anufacturer would like to thank the following for their contribution:
José González Divassón, Włodek ier-Jędrzejowicz, Bob Prosperi,
Eric Rechlin, Jake Schwartz, Namir Shammas, and Gene Wright

i
Introduction
Congratulations! You hold in your hands one of the most capable calculators
HP has ever made—the classic HP-15C, reissued and updated as the HP 15c
Collector’s Edition, the HP 15c CE. Let’s look at how this device came to be
and why its features remain in demand even today.
The Story of HP Calculators
HP introduced the world’s first scientific, pocket calculator, the HP-35, on
February 1, 1972. Single-handedly, it altered forever the market for tools
such as slide rules, books of tables, and mechanical calculators. This
calculating tool computed sine, cosine, and tangent in
degrees as well as logarithms and powers. It also
featured an independent memory register allowing a
value to be reused. The initial version, highly prized by
collectors, had a small red dot that appeared next to
the power switch whenever the calculator was turned
on. This was removed fairly soon after introduction,
since it was obvious the machine was on for two other
reasons: the on/off switch would be in the ON position
and the display would be showing a number in the red
light-emitting diode (LED) display if the batteries were
not yet discharged. For this reason, there are not many
of these early models available and they command
quite a price among collectors.
Notably, the HP-35 used Reverse Polish Notation
(RPN), allowing problems to be solved without the need for parentheses or
remembering pending operations. RPN accomplished this on the HP-35 by
using a 4-level stack where intermediate results are available and, on later
models, a fifth register named LAST X facilitating error recovery during a
calculation. Numbers were keyed in and separated using an v key. No
equals key was to be found anywhere on the keyboard.
The ease of use that RPN brought to problem solving is sometimes lost on
users today, with huge storage space and processing speeds in the gigahertz
range, but it was an incredible advance at the time. For example, consider the
fairly simple problem:
(4 + 3) ÷ (2 + 1) = ?
HP-35

ii Introduction
In RPN, the solution is to begin at the innermost set of two numbers and
proceed outward. The solution 4 v 3 + 2 v 1 + ÷ displays
the answer of 2.3333 using 9 keystrokes. Competing calculators of its day
and even for several years afterward that did not use RPN could not solve this
problem readily without a lot of parentheses. In RPN, all problems are solved
with the same approach. If you are not familiar with RPN already, time spent
with that portion of this HP 15c CE manual will pay many benefits in the
future.
HP continued to introduce more capable and updated scientific models over
the next few years, such as the HP-45 introduced on ay 1, 1973, which
added some statistical functions, conversions and multiple angular modes
for trigonometry, followed by the HP-21, introduced on February 1, 1975,
which provided the same capabilities as the HP-35 in a smaller-sized
calculator at one third the cost, a mere three years after the debut of the HP-
35.
HP also introduced a range of business models, such as the HP-80, the HP-
70, and the HP-22. These models revolutionized financial and business
calculations as much as their scientific models changed the world for
scientific and technical users, since it was now possible to solve problems
such as ones involving the time value of money on a handheld calculator.
Another revolutionary device developed by HP was the HP-65 fully
programmable pocket calculator, introduced on
January 19, 1974. Known internally at HP by the code
name “Superstar”, it was truly a game changer. The HP-
65 featured a large number of scientific functions, but
also provided users with the option to write programs
to solve new problems and add new functions to the
machine, which could be recorded and saved on
magnetic cards, so that the calculator and also your
cards with programs and data recorded on them could
all be carried with you and could even fit in a large
pocket. The 100-step program memory was huge for
the time and, even then, program execution could be
extended by reading successive program cards into the
calculator for further processing. HP-65 users were
able to submit programs they had created to the HP-65
Users’ Library where they could be shared with other users. Well over 5500
programs were submitted to the library and made available to its members
for a nominal fee. In addition, a large number of books were written, some
about techniques to use on various calculator models, but others focused on
HP-65

Introduction iii
solutions to problems in specific fields, such as navigation, astronomy,
statistics, and mathematics.
The paradigm shift created by the ability to develop your own solutions to
problems and apply them away from big corporate computers was not lost
on users of HP calculators. One such user, Richard Nelson, formed the HP-65
Users Club and began publishing a monthly journal, initially called 65 Notes.
This journal focused on documenting shorter or faster ways of solving
problems manually or with a program and got larger every month as
members of the club began submitting programs or routines they had
developed to share with others. The first programs published included
computing hyperbolic functions and their inverses while a second set used
undocumented program pointer techniques to expand the user-defined
function keys beyond the five keys at the top of the HP-65, labeled A through
E. The club later became known as PPC (Personal Programming Center),
publishing the now-renamed PPC Journal, and remained active for well over
10 years, even creating their own custom plug-in module for a later HP
calculator model. With each new HP calculator introduced, the club sought to
find new ways to extend functionality, especially through undocumented
features, and to apply these machines to new problems as power increased.
The HP-65 was followed by the fully programmable
HP-67, and its desktop sibling, the HP-97, on July 1,
1976. In some ways, however, these were more
extensions of the HP-65 than a new direction. They
provided 224 program steps, each of which could
merge several keystrokes into a single command,
rather than store each keypress as a separate step as
had been the case with the HP-65. The HP-67 and HP-
97 also added a “smart” card reader that could store
calculator status information on the cards as well as
either programs or data.
Some of the interesting new features on these models
included:
 A flag that would be set upon entering a
number from the keyboard, allowing the detection of input by the user;
 A set of 10 data registers that were exchangeable with another set of
10 data registers, referred to as primary/secondary registers; and
 The ability to write programs that would print on the HP-97 but pause
to display results on the HP-67, allowing programs written on one
model to be executed on the other without modification.
HP-6

iv Introduction
Users took advantage of this increased power by programming even more
interesting applications and games. One game program of special interest,
named Pinball Wizzard, was very popular (and yes, the author used two z’s in
the program name). HP accepted programs for the HP-67 and HP-97 into the
HP-67/97 Users’ Library, which ended up containing over 4800 submitted
programs.
Due to their more capable programming features and lower price point
compared to the earlier HP-65, these two new models were also widely
adopted by professionals and companies for specialized uses. The HP-67 was
sold for over 5 years while the HP-97 was sold for over 8 years. These models
certainly filled a need.
eanwhile, HP had been developing another line of smaller programmable
calculators that did not include the ability to save programs externally. The
first of these, still remembered fondly by all who
owned one, was the HP-25, introduced on August 1,
1975. While this model only had 49 fully-merged
program steps, its small size and well-rounded feature
set created many fans. The PPC Journal published a
user-created collection of 56 programs for this model,
addressing topics from probability distributions such
as normal, binomial, hypergeometric, to math
functions such as the Bessel, Error, Gamma, and more.
Users also wrote a wide range of game programs to run
in this little marvel, such as bagels, subhunt, roulette,
blackjack, slot machine, and more.
Following the HP-25 came the HP-25C, the first
handheld calculator model with a letter at the end of
the name. Earlier HP products were normally referred
to by a number followed by a letter. With HP’s calculators, the naming was
different, and models had two digits. After the introduction of the HP-25C,
nearly all models were named with one or two digits followed by one or two
letters.
As a historical note, the letter A was the standard letter at the end of a
calculator model number, although it was not explicitly used in calculator
advertisements or manuals. So for instance, the original HP-35 was officially
the HP-35A, but was not normally referred to as such. The letter B eventually
referred to business models, C referred to a continuous memory model. The
letter E was used for the series E models discussed below (E for “Easy”—easy
to assemble as the original versions clicked together with a minimum of
HP-25C

Introduction v
solder used in their assembly). The letter S was used for scientific models,
such as the later HP 35s model. Some updated models have the symbol + or
the Roman numeral II added at their end. A few even have both, such as the
HP 10bII+. This makes for a wide range of naming conventions!
The newly introduced HP-25C added continuous memory to the already
successful original HP-25 model. While the HP-65 and HP-67 could store
programs and data on magnetic cards, the HP-25 did not have a card
reader/writer. When turned off, the calculator lost any data or programs that
had been loaded. The HP-25C used an entirely new chip design process from
HP that allowed it to save programs and data even when turned off. It is
difficult to overstate users’ amazement at first seeing a device remember
things when turned off—something that is taken for granted today.
On July 1, 1977, HP introduced the successor to the HP-25C, named the HP-
29C, along with a printing version of this model two months later, the HP-
19C. The HP-29C model was the same size and shape as the HP-25C, but
doubled the available program memory and added incremental
programming and math functions. While a great machine in its own right, this
model had a relatively short time in the limelight due to the advancement of
technology and capability being built into each new calculating device.
On April 17, 1978, HP announced the Series E machines, designed as a family
of less expensive models. They ranged from an
inexpensive scientific model (the HP-31E) to a 49-
step programmable (the HP-33E) to two financial
calculator models (the HP-37E and HP-38E—the
latter of which was programmable too) following in
the footsteps of earlier finance machines.
On July 16, 1979, HP introduced a new computing
standard, a top-of-the-line model serving as the
heart of a computing system, the HP-41C, the first HP
handheld calculator with a Liquid Crystal Display
(LCD) and the ability to display letters as well as
numbers. This model led down the path of additional
advanced RPN models such as the HP-42S but also
the transition to RPL (standing for Reverse Polish Lisp
or RO -based Procedural Language) models such as
the HP 48SX, HP 48GX, HP 49G, HP 49g+, and the HP
50g. HP then introduced the HP Prime in 2014, their most capable, powerful
calculator ever made. That, however, is a story for another time.
HP-41C

vi Introduction
On August 15, 1979, HP announced updates to the HP-33E and HP-38E
models to include continuous memory (named the HP-33C and HP-38C). HP
also announced the HP-34C, an entirely new model in the Series E calculator
family. This model, like those that had gone before, was programmable, but
did not have external storage. Instead, it too relied upon continuous memory
to retain programs and data. The HP-34C was able to adjust memory between
program and data storage. The default was to have 70 bytes of program
memory space and 21 data registers. These data registers would be
converted to program memory automatically as a user entered a longer
program, up to the point of having 210 program bytes available with one
permanent data register remaining.
The HP-34C incorporated new, built-in features that were never before
available on a handheld calculating device. The HP-34C included a
generalized solve feature. Users would enter a program evaluating a function
and when _ was executed, it would attempt to find a value where the
function was equal to zero—a root of the function.
For example, the user can write a short program to
evaluate x2 - 4 and then input a range between 1 and
5 as an estimate for the root, and then execute
_. A result of 2 is returned for the root, a value
of x where the function is equal to zero. No previous
calculator had ever had a built-in function that would
do this so easily, although programs had previously
been written to do it.
The other groundbreaking feature on the HP-34C was
the ability to numerically integrate a function entered
as a program, between an upper and a lower limit.
There had been long user programs written in the past
that would apply various approaches to evaluating an
integral numerically, but the HP-34C was designed to
evaluate the numeric integral of any user-entered program if at all possible.
Thus if a short program were entered that computed 1/x, the user could enter
a lower and upper limit of integration, say 1 and 6, and then execute the f
function on the keyboard. The HP-34C would perform the integration if
possible, in this case displaying 1.7918 to four decimal places, the natural log
of 6, the correct answer.
Whole classes of problems could now be solved on a handheld calculator with
an ease of use that had never been seen before. The problem was that this
calculator, and all the other models previously introduced other than the HP-
HP-34C

Introduction vii
41C, were usually tied to a short period of use before needing to be plugged
into an outlet and recharged due to those lovely, but power-hungry red LED
displays. If only there were a way to _ that problem!
HP solved that problem on the remaining
models with the introduction on
September 1, 1981, of their new slimline
series of calculators, codenamed
Voyager, beginning with the HP-11C and
HP-12C. While the HP-11C was
discontinued in early 1989, the HP-12C
became such a standard in the financial
sector that it has been continuously sold
for over 41 years as of this writing.
Ten months after the HP-11C and HP-12C, HP introduced the HP-15C and the
HP-16C on July 1, 1982—two new models with the same shape and size.
The HP-16C was aimed at systems programmers and appropriately named
the “Computer Scientist” by HP. The brochure for this model began: “The
most powerful calculator ever designed for computer science and digital
electronics applications” and that it was. The HP-16C had four number bases
(binary, octal, decimal, and hexadecimal), four Boolean operators (AND, OR,
XOR [Exclusive OR], and NOT),
extensive bit manipulation abilities,
and variable word size (up to 64 bits),
plus one’s and two’s complements.
An example in the HP-16C Owner’s
Handbook included a program to
convert between IEEE standard
floating-point binary format and the
floating-point decimal format used in
the HP-16C itself. Programming
abilities included a maximum of 203 program lines or 101 16-bit data
registers, in addition to 16 program labels, 4 levels of subroutines, 6 flags,
and 8 conditional tests. It is still in high demand in its niche on the used
market…if you can find one!
HP-12C
HP-16C

viii Introduction
The HP-15C
eanwhile the HP-15C took the groundbreaking features of the HP-34C,
including the root solver and numerical integration, expanded them, and
placed them into a slimline LCD package with incredible battery life. It
could be taken anywhere and seemed to run forever on one set of
batteries. It expanded upon the features of the HP-34C by:
 Increasing program and data storage space;
 Providing annunciators in the display indicating calculator status;
 Featuring a U mode, where the first five keys at the top left can
begin the program execution of the label written above the key
rather than perform the function on the key;
 Computing hyperbolic trigonometry functions and their inverses;
 Adding combinations, permutations, and a random number
generator;
 Extending the function set to work with complex numbers where
possible;
 Introducing a broad array of matrix functionality;
 Fitting it all in a four-ounce device.
The HP-15C had roughly twice the memory of the earlier HP-34C, with 67
total registers available for use as program or data. On the HP-15C, three
registers were permanently allocated for data storage, but the remaining
64 registers could be set aside for
data usage in any combination from 0
to 64, with registers being used for
program storage at the rate of 7 bytes
per register.
When placed in complex number
mode, the HP-15C’s four level RPN
stack extended to handle the real and
imaginary portions of a complex
number entered for computation—essentially creating a parallel stack
for the imaginary part of each complex number. Adding two complex
numbers together was therefore just as easy as adding two real numbers.
In fact, about the only mathematical operations that did not work with
complex numbers were the polar to rectangular conversion and its
inverse. Complex numbers were no longer complex at all.
HP-15C

Introduction ix
atrix functionality was built in to handle up to an 8 × 8 matrix. Functions
provided included finding determinants, inverses, LU decomposition,
scalar and matrix arithmetic, transpose, solving systems of equations,
norms, residuals, and transformations. These abilities were not lost on
students and professionals alike. The HP-15C remained highly popular!
Nevertheless, as technology moved on, HP replaced the HP-15C with a
range of later models. These had more features and greater speed than
the HP-15C, yet users yearned for the HP-15C’s particular characteristics,
including the horizontal layout. Prices for secondhand units rose steadily,
and former users pressed HP to bring the HP-15C back. After all, if HP
continued to make the HP-12C, could they not use the same basic model
to build a revived HP-15C? In 2011 HP did produce a limited number of HP-
15C units, described as the HP 15c Limited Edition.
The HP 15c Collector’s Edition
Now, a further 12 years later, you have in your hands a second revival: the
HP 15c Collector’s Edition. Yet it is not just for collectors—it is a powerful
calculator in its own right, faster and with more memory than the original
HP-15C. The HP 15c CE now provides:
 672 bytes of program memory (one or two bytes per instruction),
increased from 448, while retaining the HP-15C’s sophisticated
programming capability, including conditional and unconditional
branching, subroutines, flags, and editing.
 Direct and indirect storage in up to 99 registers, increased from 67.
In general the extra memory and speed are an advantage, but there will
be some cases where care is needed:
 If a program written for the original HP-15C relies on special timing,
for example if a program gives the user a fixed time to react, then
that program will need to be slowed down on the HP 15c CE,
possibly by the addition of © (pause) steps or by making loops
repeat more times. This is described in more detail in Appendix G.
 The original self-tests for the HP-15C will not work with the new
platform of the HP 15c CE and have been replaced with new tests
described in Appendix F.

x Introduction
This Handbook
HP calculators of the 1970s and the 1980s were not just technological feats.
They were supported by manuals that were feats of technical writing. The
manuals introduced the features of the calculator and supported the reader
with varied examples of use. Some of these examples were whimsical and
added to the joy of reading the manuals. One particular example
remembered by HP enthusiasts was in the HP-25 manual, and concerned
lovesick sailor Oscar Odysseus, who found himself on the remote island of
Tristan da Cunha. The example showed owners how to use the HP-25 to
calculate the great circle distance to his sweetheart Penelope on St Helena.
This handbook is written for you, regardless of your level of expertise. The
first part, Fundamentals, covers all the basic functions of the HP 15c and how
to use them. Each section in the second part, Programming, is broken down
into three subsections—The echanics, Examples, and Further
Information—in order to make it easy for users with varying backgrounds to
find the information they need. The third part, Advanced Functions, 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.
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.
We hope that you will enjoy working through this manual for the HP 15c CE,
and through its companion, the HP 15c Advanced Functions Handbook, which
provides further details, particularly of the _ and f (Integrate)
functions, but also of complex number and matrix calculations. In that
handbook, you will find examples involving people such as radio engineer
Ann Tenor—as well as programs equivalent to the Time Value of oney and
Discounted Cash Flow Analysis applications built into HP’s financial
calculators. These are long programs, but with the increased memory size of
the HP 15c CE you can keep them in your calculator and use it as a substitute
for an HP-12C business calculator as well as for scientific and technical
calculations.
*
You certainly do not need to read every part of the manual before delving into Part III: HP
15c Advanced Functions if you are already familiar with HP calculators. The use of
_ and f requires a knowledge of HP 15c programming.

Introduction xi
The HP Community
One of the benefits of owning an HP calculator is that there are large numbers
of people like you who own one as well. In fact, there are still active groups
and websites where users gather in person and virtually. These sites and
groups can be sources of great information and can often provide answers to
questions. Some of the most helpful sites include:
 hpcc.org – This is the website for a group of users that has been in
existence since 1982, centered in London, England, and which still
publishes a journal of articles, application programs, and other
material. Back issues are available as well. The group also holds
regular meetings online and in person.
 hhuc.us – This site contains information about the HP handheld users’
conferences in the US since 1999. These meetings continue to be held
and information about future conferences can be found there.
 hpmuseum.org – In addition to being an online museum for HP
calculators where you can look up a favorite model from the past, this
site has a very active discussion forum about current and older HP
calculator models, things related to HP calculators, or things
completely unrelated to HP calculators. There is also a section of the
forum devoted to software for various HP calculators containing user-
submitted programs.
 commerce.hpcalc.org – This site offers a USB thumb drive with more
than ten years’ worth of PPC Journal issues mentioned earlier along
with an incredible amount of other calculator documentation and
materials. It also contains copies of the presentations made at
previous HP handheld users’ conference gatherings. Check there for
more information.
 literature.hpcalc.org – This site has scans of a large number of HP
calculator manuals and training materials as well as of non-HP
materials, including books, in several different languages. Be sure to
check it out.
Note: None of the above sites are in any way associated with HP.
If you have a question or wish to see if someone has already found a solution
to a problem you are facing, check these resources out.
So enjoy this updated version of a true classic. There are always new
problems to be solved and the HP 15c CE is ready and able to help!
February, 2023
Włodek ier-Jędrzejowicz Gene Wright
Chairman, hpcc.org oderator, hpmuseum.org/forum

4
Contents
The HP 15c: A Problem Solver ........................................................ 12
A Quick Look at v ............................................................... 12
anual 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
The Automatic emory Stack and Stack anipulation ............... 32

Contents 5
Stack anipulation 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
ean ........................................................................................... 53
Standard Deviation .................................................................... 53
Linear Regression ...................................................................... 54
Linear Estimation and Correlation Coefficient .......................... 55
Other Applications ..................................................................... 56
Section 5: The Display and Continuous Memory ........................... 58
Display Control .............................................................................. 58
Fixed Decimal Display ................................................................ 58
Scientific Notation Display ......................................................... 58
Engineering Notation Display .................................................... 59
antissa 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 emory ...................................................................... 62
Status ......................................................................................... 62
Resetting Continuous emory .................................................. 63
Adjusting Display Contrast ........................................................ 63

6 Contents
Part II: HP 15c Programming ............................................. 65
Section 6: Programming Basics .................................................. 66
The echanics .............................................................................. 66
Creating a Program ................................................................... 66
Loading a Program .................................................................... 66
Intermediate Program Stops .................................................... 68
Running a Program .................................................................... 68
How to Enter Data ..................................................................... 69
Program emory ....................................................................... 70
Example ........................................................................................ 70
Further Information ...................................................................... 74
Program Instructions ................................................................ 74
Instruction Coding ..................................................................... 74
emory Configuration .............................................................. 75
Program Boundaries ................................................................. 77
Unexpected Program Stops ...................................................... 78
Abbreviated Key Sequences ...................................................... 78
User ode .................................................................................. 79
Polynomial Expressions and Horner’s ethod ......................... 79
Nonprogrammable Functions ................................................... 80
Problems ....................................................................................... 81
Section : Program Editing ............................................................ 82
The echanics .............................................................................. 82
oving to a Line in Program emory ....................................... 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 echanics .............................................................................. 90
Branching ................................................................................... 90
Conditional Tests ....................................................................... 91

Contents
Flags ........................................................................................... 92
Examples ....................................................................................... 93
Example: Branching and Looping .............................................. 93
Example: Flags ........................................................................... 95
Further Information ...................................................................... 97
Go To .......................................................................................... 97
Looping ...................................................................................... 98
Conditional Branching ................................................................ 98
Flags ........................................................................................... 98
The System Flags: Flags 8 and 9 ............................................... 99
Section 9: Subroutines .................................................................... 101
The echanics ............................................................................... 101
Go To 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 echanics ............................................................................... 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: I and 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
I and e ........................................................................... 116
Indirect Display Control ............................................................. 116

8 Contents
Part III: HP 15c Advanced Functions ............................. 119
Section 11: Calculating With Complex Numbers .......................... 120
The Complex Stack and Complex ode ....................................... 120
Creating the Complex Stack ...................................................... 120
Deactivating Complex ode ...................................................... 121
Complex Numbers and the Stack ................................................. 121
Entering Complex Numbers ...................................................... 121
Stack Lift in Complex ode ....................................................... 124
anipulating 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 anipulation 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
atrix Dimensions ........................................................................ 140
Dimensioning a atrix ............................................................... 141
Displaying atrix Dimensions ................................................... 142
Changing atrix Dimensions ..................................................... 142
Storing and Recalling atrix Elements ........................................ 143
Storing and Recalling All Elements in Order ............................. 143
Checking and Changing atrix Elements Individually .............. 145
Storing a Number in All Elements of a atrix ........................... 147
atrix Operations ......................................................................... 147
atrix Descriptors ..................................................................... 147
The Result atrix ...................................................................... 148
Copying a atrix ........................................................................ 149
One- atrix Operations .............................................................. 149