HP RPN SCIENTIFIC WP 34S User manual
Edition 3.1
Page 1 of 211
MANUAL
This manual documents WP 34S. WP 34S is free software: you can
redistribute it and / or modify it under the terms of the GNU General
Public License as published by the Free Software Foundation, either
version 3 of the License, or (at your option) any later version.
WP 34S is distributed in the hope that it will be useful, but without any
warranty; without even the implied warranty of merchantability or fit-
ness for a particular purpose. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with WP 34S. If not, please see http://www.gnu.org/licenses/ .
This manual contains valuable information. It was designed
and written in the hope it will be read thoroughly by you.
For really quick and impatient users, however, there is a stand-alone
two-page Troubleshooting Guide starting on page 180 of this manual.
This manual may change without notice if we, the developers, modify WP 34S. We reserve the right to do so
at any time. The cover picture may stay unchanged the document status can be seen from the last note on
last page. We recommend you watch http://sourceforge.net/projects/wp34s/develop to stay informed.
Updated Edition 3.3
Edition 3.1
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WP 34S would not have reached its present state without our love for Classics, Woodstocks, Spices, Nuts,
Voyagers, and Pioneers. Thus we want to quote what was printed in HP pocket calculator manuals until
1980, so it will not fade:
“The success and prosperity of our company will be assured only if we offer our customers
superior products that fill real needs and provide lasting value, and that are supported by a
wide variety of useful services, both before and after sales.”
Statement of Corporate Objectives.
Hewlett-Packard
... you do not have your WP 34S calculator yet: WP 34S runs on an HP-20b Business Consultant or an
HP-30b Business Professional. Both are financial pocket calculators. So if one of those is sitting on your
desk unchanged as produced for HP, please turn to Appendix A for instructions how to convert it into a full-
fledged WP 34S yourself. On the other hand, if you do not want to bother with cables on your desk
connecting it to your computer, with flashing the calculator firmware and attaching a sticky overlay, you can
purchase an HP-30b-based WP 34S readily on the internet; see e.g. http://commerce.hpcalc.org/34s.php or
http://www.thecalculatorstore.com/epages/eb9376.sf/en_GB/?ObjectPath=/Shops/eb9376/Products/%22WP34s%20Pack%22 .
The first way (doing it yourself) will just cost you some time, the second will cost you some money. If you
choose buying your WP 34S at one of the sites mentioned, we (the developers) will get a very modest
fraction of the price to support our otherwise unpaid efforts on the WP 34S project. Either way will work it is
your choice.
Furthermore, there are three optional hardware modifications requiring some fine soldering, cutting,
gluing, and drilling a little hole in the plastic case of your business calculator. It is no sorcery for a
young electronics engineer with a slow hand and good eyesight, but might come close to it for others
(including me, W.B.). So check Appendix H and decide whether you want to do that yourself. Else look
for somebody who is able to do it for you.
The WP 34S package includes a full size emulator, so you may test it on your computer before buying any
hardware. And later on, you may test your programs there as well before sending them to your WP 34S. The
function sets are identical.
For the following, we assume the conversion is done and you hold your WP 34S in your hands.
Original Edition 3.1: © 2012 by Walter Bonin
Updated Edition 3.3: © 2016 by Franz Huber
Edition 3.1
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TABLE OF CONTENTS
Welcome!................................................................................................................7
Print Conventions and Common Abbreviations ....................................................9
Getting Started......................................................................................................10
Keyboard Basics................................................................................................11
Entering Numbers ..............................................................................................15
Real Calculations ...............................................................................................16
Elementary Stack Mechanics .............................................................................17
Error Recovery...................................................................................................21
Calling Commands Unseen on the Keyboard.....................................................22
Addressing Objects...............................................................................................24
The Virtual Keyboard for Addressing Transient AT).....................25
Addressing Real Numbers..................................................................................26
Real Matrices and Vectors .................................................................................28
Complex Calculations.........................................................................................29
Addressing Complex Numbers...........................................................................33
Your WP 34S in Various Operating Modes...........................................................35
The Display........................................................................................................35
Recognizing Calculator Modes...........................................................................36
Common Commands Returning Specific Displays: STATUS, VERS, ERR, etc..38
Floating Point Modes 1: Introduction and Localisation ....................................39
Floating Point Modes 2: Displaying Decimal Numbers, Fractions, Times, etc. 40
Floating Point Modes 3: Real Statistical Calculations......................................45
Integer Modes 1: Introduction and Virtual Keyboard.....................................52
Integer Modes 2: Displaying Integer Numbers .............................................53
Integer Modes 3: Bitwise Operations ...........................................................56
Integer Modes 4: Integer Arithmetic.............................................................58
Full Alpha Mode 1: Introduction and Virtual Keyboard..................................61
Full Alpha Mode 2: Displaying Text..............................................................64
Programming Your WP 34S..................................................................................66
Labels ................................................................................................................67
Tests..................................................................................................................67
Local Data..........................................................................................................69
Programmed Input and Output, User Interaction and Dialogues.........................69
Keyboard Codes and Direct Keyboard Access...................................................71
Flash Memory (FM) and XROM..........................................................................72
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Index of Operations (IOP).....................................................................................74
A ........................................................................................................................76
B ........................................................................................................................77
C........................................................................................................................78
D........................................................................................................................81
E ........................................................................................................................83
F.........................................................................................................................85
G........................................................................................................................86
H........................................................................................................................88
I..........................................................................................................................88
J.........................................................................................................................89
K ........................................................................................................................89
L.........................................................................................................................89
M........................................................................................................................92
N........................................................................................................................94
O........................................................................................................................95
P ........................................................................................................................95
R........................................................................................................................97
S ......................................................................................................................100
T.......................................................................................................................105
U......................................................................................................................105
V ......................................................................................................................106
W .....................................................................................................................106
X ......................................................................................................................107
Y ......................................................................................................................108
Z.......................................................................................................................108
.......................................................................................................................109
.......................................................................................................................111
.......................................................................................................................111
.......................................................................................................................111
.......................................................................................................................111
.......................................................................................................................111
......................................................................................................................111
.......................................................................................................................112
......................................................................................................................113
.......................................................................................................................113
The Rest ..........................................................................................................113
Nonprogrammable Control, Clearing and Information Keys..............................119
Alphanumeric Input ..........................................................................................123
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Catalogs and Browsers.......................................................................................125
Catalog Contents in Detail................................................................................130
Accessing Catalog Items the Fast Way............................................................133
Constants (CONST).........................................................................................134
Unit Conversions (CONV) ................................................................................139
Predefined Global Alpha Labels (CAT).............................................................143
The Stopwatch Application .................................................................................145
Appendix A: Setup and Communication .............................................................147
How to Flash Your HP-20b or HP-30b..............................................................147
Overlays Where to Get Them and How to Make Them Yourself if Required..151
Updating Your WP 34S....................................................................................152
I/O Overview ....................................................................................................153
Appendix B: Memory Management.....................................................................154
Status and Configuration Data .........................................................................154
Global Registers...............................................................................................154
Summation Registers.......................................................................................156
Subroutine Return Stack (SRS) and Program Memory.....................................156
Making Room for Your Needs ..........................................................................157
Addressing and Accessing Local Data, Recursive Programming......................158
Switching between Standard Real (SP) and Integer Modes .............................159
Appendix C: Messages and Error Codes............................................................162
Appendix D: The WP 34S Emulator on Your Computer......................................165
Data Transfer between Your WP 34S and Your Computer...............................166
Mapping of Memory Regions to Emulator State Files.......................................168
Simulating a Printer on Your Computer............................................................168
Appendix E: Character Sets................................................................................169
Appendix F: Corresponding Operations to the HP-42S and -16C Function Sets 172
HP-42S ............................................................................................................172
HP-16C............................................................................................................178
Appendix G: Troubleshooting Guide...................................................................180
Overcoming Troubles in Calculator Operation..................................................180
Overcoming Flashing Troubles.........................................................................182
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Appendix H: Additional Information for Advanced Users ....................................184
Changing Word Size in Integer Modes.............................................................184
Mode Storing and Recalling .............................................................................184
Commands for Advanced Users.......................................................................185
Double Precision (DP) Calculations and Mode Switching.................................186
Further Commands Used in Library and XROM Routines ................................189
Assembler Output ............................................................................................191
Basic Electrical Hardware Specifications of the HP-20b and HP-30b...............191
Tuning the Hardware of Your WP 34S..............................................................192
Appendix I: Advanced Mathematical Functions ..................................................198
Numbers ..........................................................................................................198
Statistical Distributions.....................................................................................199
More Statistical Formulas.................................................................................204
Orthogonal Polynomials ...................................................................................207
Even More Mathematical Functions .................................................................208
Appendix J: Release Notes.................................................................................210
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WELCOME!
Dear user, now you have got it: your very own WP 34S. It uses the mechanics and
hardware of an HP-20b Business Consultant or an HP-30b Business Professional, re-
spectively, so you benefit from the excellent processor speed of these pocket calculators.
And with an HP-30b you also get the famous rotate-and-click keys, giving you the tactile
feedback that has been appreciated in vintage Hewlett-Packard calculators for decades.
On the other hand, the firmware and user interface of your WP 34S were thoroughly
thought through and discussed by us, newly designed and written from scratch, loaded
with functions, pressed into the little memory available, and tested over and over again to
give you a fast and compact scientific calculator like you have never had before
fully keystroke programmable, comfortably fitting into your shirt pocket, and RPN1.
The function set of your WP 34S is based on the famous HP-42S RPN Scientific of 1988,
the most powerful programmable RPN calculator industrially built so far.2We expanded
the set, incorporating the functions of the renowned computer scientist HP-16C, the
fraction mode of the HP-32SII, and probability distributions similar to those of the HP-21S.
We also included numerous additional useful functions for mathematics, statistics,
physics, engineering, programming, I/O, etc., such as
+ and functions, Bernoulli and Fibonacci numbers,
, the error function, and the Chebyshev, Hermite, Laguerre, and
Legendre orthogonal polynomials (no more need to carry heavy printed tables),
+many statistical distributions and their inverses: Poisson, Binomial, Geometric,
Cauchy-Lorentz, Exponential, Logistic, Weibull, Lognormal, and Gaussian,
+programmable sums and products, first and second derivatives, solving quadratic
equations for real and complex roots,
+testing for primality,
+integer computing in fifteen bases from binary to hexadecimal,
+extended date and time operations and a stopwatch3based on a real-time clock,
+financial operations such as mean rate of return and margin calculations,
+88 conversions, mainly from old Imperial to universal SI units and vice versa,
+50 fundamental physical constants as accurate as used today by national standards
institutes such as NIST or PTB, plus a selection of important constants from
mathematics, astronomy, and surveying,
+bidirectional serial communication with your computer, as well as printing on an HP
82240A/B 4,
+battery-fail-safe on-board backup memory,
+Greek and extended Latin letters covering the languages of almost half of
population (upper and lower case in two font sizes), plus mathematical symbols.
1 RPN stands for reverse Polish notation, a very effective and coherent method of calculating (see p. 15).
2The matrix menu of the HP-42S cannot be supported by WP 34S for hardware reasons. Your WP 34S
features a set of basic matrix commands and several library routines dealing with matrices instead.
3The stopwatch requires adding a quartz crystal and two tiny capacitors.
4Printing requires adding an IR diode and a resistor. Even a USB board is available for your WP 34S.
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WP 34S is the first RPN calculator overcoming the limits of a four-level stack
stop worrying about stack overflow in calculations. WP 34S features a choice of two stack
sizes expanded by a complex LASTx register: traditional four stack levels for HP
compatibility, eight levels for convenient calculations in complex domain, for advanced real
calculus, vector algebra in 4D, or whatever application you have in mind. You will find a full
set of commands for stack handling and navigation in either stack size.
Furthermore, your WP 34S features up to 107 global general purpose registers, 112 global
user flags, up to 928 program steps in RAM, up to 6014 program steps in flash memory, a
30 byte alpha register for message generation, 16 local flags as well as up to 144 local
registers allowing for recursive programming, and 4 user-programmable hotkeys for your
personal favorite functions. Most of the memory layout is conveniently user-settable.
WP 34S is the result of a collaboration of two individuals, an Australian and a German, that
started in 2008. We developed WP 34S in our free time so you may call it our hobby
(although some people close to us found other names for it). From the very beginning, we
have discussed our project in the forum of the Museum of HP Calculators. We would like
to thank all its international members, who taught us a lot and contributed their ideas and
lent their support throughout several stages of our project. Special thanks go to Marcus
von Cube (Germany) who joined us in bringing WP 34S to life by designing an emulator for
v1.14, allowing for widespread use and convenient testing. Starting with v1.17, the
software began running on an HP-20b hardware. A very useful assembler/disassembler
has been provided by Neil Hamilton (Canada) since v1.18 even a symbolic preprocessor
has been added since v2.1. For v3.0, Pascal Méheut (France) contributed a versatile
flashing tool for various operating systems. With v3.1, printing on an HP82240A/Bprinter
became possible thanks to the gracious support by Christoph Gießelink (Germany); a set
of micro USB boards was developed by Harald Pott (Germany); Ciaran Brady (UK) wrotea
Beginner’sGuide for our WP 34S,and Christian Tvergaard and Peter Murphy (both USA)
carefully proofread this manual. We greatly appreciate all your support!
We named our baby WP 34S in honor of the HP-34C from 1979, one of the most powerful
compact LED pocket calculators. WP 34S is our humble approach within the constraints
of HP’s hardware to a future 43S we can only dream of succeeding the HP-42S at one
point. May our project help to convince those that have access to more resources than we
do: Catering to the market for serious scientific instruments is well worthwhile!
We carefully checked all aspects of WP 34S to the best of our ability. Our hope is that
WP 34S is free of severe bugs. However, this cannot be guaranteed. We promise to
continue improving WP 34S whenever necessary. If you discover any strange results,
please report them to us. If they turn out to be caused by internal errors, we will provide
you with an update as soon as it is available. Just as before, we will continue striving to
maintain short response times.
Enjoy!
Paul Dale and Walter Bonin
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Print Conventions and Common Abbreviations
Throughout this manual, standard font is Arial. Emphasis is added by underlining or bold
printing. Specific terms, titles, trademarks, names or abbreviations are printed in italics,
hyperlinks in blue underlined italics. Bold italic letters such as nare used for variables;
constant sample values (e.g. of labels or displayed characters) use bold normal letters.
Calculator COMMANDS are generally called by their names, printed in capitals in running
text.
This font is taken for explicit references to calculator keys. Alphanumeric and numeric
displays (such as Hello! and 12,34 ) are quoted using the respective calculator fonts
where applicable and beneficial.
Courier is employed for file names and numeric formats.
Register ADDRESSES are printed using bold Times New Roman capitals, while register
contents are expressed by lower case bold italics. So e.g. the value ylives in stack register
Y, r45 in general purpose register R45, and alpha in the alpha register. Overall stack
contents are generally quoted in the order [ x, y, z . Lower case normal italics are for
units.
All this holds unless stated otherwise.
The following abbreviations are used at various locations in this manual:
DP = double precision (see p. 186).
FM = flash memory (a special kind of RAM, see p. 72).
IOP = index of operations (see p. 74).
IR = infrared.
LCD = liquid crystal display.
RAM = random access memory, allowing read and write operations.
ROM = read-only memory, allowing only read operations.
SP = single precision (see p. 159).
USB = universal serial bus, i.e. a specific interface.
XROM = extended ROM (see p. 72).
Some more abbreviations may be used locally.
Finally: WARNING indicates the risk of severe errors. There are only four warnings printed in this
manual. Locking up your calculator is the worst that can happen to it, as far as we know.
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GETTING STARTED
If you know how to deal with a good old Hewlett-Packard RPN scientific calculator,
you can start using your WP 34S almost right away. Use this manual to get
information on some basic design concepts that put your WP 34S ahead of previous
RPN calculators. Continue using this manual for reference.
On the other hand, if this is your first RPN scientific calculator at all or the first you
use for a long time, we recommend you get an HP-42S Owner’s Manual. It is
available at low cost on a DVD distributed by the Museum of HP Calculators (see
here: http://www.hpmuseum.org/cd/cddesc.htm ).
Read part 1 of said manual as a starter. It includes an excellent introduction to RPN.
RPN is the reason why your WP 34S works without an key; nor does it need the
keys nor . Once you got used to RPN you may never choose a calculator
featuring again.
Part 2 of the HP-42S Owner’s Manual will help you programming your WP 34S for
quick and easy solving lengthy, repeated or iterative computations.
Further documentation, including complete information about the other vintage calcu-
lators and the famous PPC ROM mentioned in this manual, is readily accessible on
said DVD, too.
Alternatively to the HP-42S Owner’s Manual, you can download a dedicated WP 34S
Beginners Guide, recently written by one of our users:
http://sourceforge.net/projects/wp34s/files/doc/WP_34S_Beg_Guide.pdf .
Most traditional commands on your WP 34S will work as they did on the HP-42S. This little
manual here is meant as a supplement presenting all the new features. It contains the
necessary information about them, including equations and technical explanations; it is not
intended, however, to replace textbooks on mathematics, statistics, physics, engineering,
or programming, nor is it a hypothetical Beginner’s Guide to RPN Computing.
Your WP 34S is designed to help you in your calculations and computations.
But it is just a tool although a very powerful one it cannot think for you nor can it
check the sensibility of a problem you apply it to. Do not blame us nor your WP 34S
for errors you have made. Gather information, think before and while keying in, and
check your results: these will remain your responsibilities always.
The following text starts with presenting you the user interface, so you learn where you will
find what you are looking for. It continues by demonstrating some basic methods, the
WP 34Smemory and addressing items therein, and the display and indicators that give
you feedback about what is going on. Then the major part of this manual consists of an
index of all available operations and how to access them, and of lists of all catalog
contents. This manual closes with appendices covering special topics, e.g. a list of error
messages your WP 34S will return if abnormal conditions prevent it from executing your
command as expected. There you will also find instructions for keeping your WP 34S up-
to-date when new firmware revisions appear.
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Keyboard Basics
Start exploring your WP 34S: Press its bottom left key to turn it on notice that .ON.is
printed below that key. If you turn on your WP 34S the very first time, you will get what you
see displayed below. To turn it off again, press the green key (notice a little ⓗshowing
up top left in display), then (which has OFF printed on its lower part). Since your
WP 34S has Continuous Memory, turning it off does not affect the information it contains.
To conserve battery energy, your WP 34S will shut down some five minutes after you stop
using it when you turn it on again, you can resume your work right where you left off.
To adjust display contrast, hold down .ON.while you press or .
Look at the keyboard of an HP-42S for
comparison. The most striking differ-
ence to it is the colorful surface of your
WP 34S. You get five functions per
key on average. White print on key top
is for the primary function of the key.
For secondary functions, green labels
are put on the slanted lower faces of
34 keys, golden and blue labels are
printed below them on the key plate.
Grey letters are bottom left of 26 keys.
To access a white label, just press the
corresponding key (thus it is called
primary function). For a golden, blue,
or green label, press the prefix ,
, or , respectively, then the
corresponding key.
Take the key for example. Press-
ing
will enter the digit 5 in display,
+ will calculate the arithmetic
mean values of data accumulated in
the statistic registers via ,
+ will compute the standard
deviations for the same data via ,
+ will open a catalog (i.e. a
set) of extra statistical functions via
. All labels printed underlined
on the keyboard point to catalogs.
The grey Rwill become relevant in
alpha mode, i.e. for input of text.
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, , and allow for easily accessing a multiple of the 37 primary functions this
hardware can take. The active prefix is indicated by ⓕ, ⓖ, or ⓗtop left in the display for
visual feedback, if applicable. You may hold down , , or if you want to call
several functions in sequence showing the same color.
Time for a little problem solving example. Turn your WP 34S on again if necessary (it
may have shut down automatically in the meantime). Anyway it will still show its last
display
5.
Now let us assume you want to fence a little rectangular patch of land, 40 yards long
and 30 yards wide.6You have already set the first corner post (A), and also the
second (B) in a distance of 40 yards from A. Where do you set the third and fourth
post (C and D) to be sure that the fence will form a proper rectangle? Simply key in
This key separates the two numbers in
input here.7
Note is reached by pressing
+ top right on the keyboard.
So, just get 80 yards of rope, nail its one end on post A and its other end on B, fetch
the loose loop and walk 30 yards away. When both sections of the rope are tightly
stretched, stop and place post C there. You may set post D the same way.
This method works for arbitrary rectangles: whatever other distances may apply in
your case. As soon as you press , your WP 34S does the necessary calculation
of the diagonal automatically for you. You just provide the land, posts, rope, hammer
and nails. And it will be up to you to set the posts!
5 If your WP 34S fails to show this display for any reason whatsoever (e.g. because you played around with it
a bit in the meantime), you will get it by sliding the battery cover open, locating the little hole below the label
RESET, and actuating the button behind it using a suitable pin. Then close the cover again and press .
6This manual is written for an international readership, and we very well know the SI system of units agreed
on internationally and adopted by almost all countries on this planet. Despite this fact, we use (old British)
Imperial units here so our US-American readers can follow. But the example will work with meters as well.
7Note the number 40 being adjusted to the right and a radix mark added. This indicates input being closed
for this number.
Generally, we shall quote only numeric displays in the following for space reasons, using the proper font.
And for better readability on paper, we refer to keyboard labels using dark print on white like e.g. or
, omitting the prefix for the latter since redundant by color print. Also we will use points as radix
marks, although significantly less visible than commas, unless specified otherwise explicitly. By experience,
versa.
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As you have found on the keyboard next to two other labels showing arrows as well,
the labels on your WP 34S are generally grouped according to their purposes. Generally,
functions and their inverses if existent are placed next to each other. If a function is
called using , its inverse is called using . Besides
the keys for numeric input ( , , , , , , , , and ),
the three prefixes explained so far ( , , and ), and
the four elementary arithmetic operations ( , , , and ),
there are five larger groups of labels as outlined below:
Mathematical
functions typ-
ically working
with real
numbers
Probability
and statistics
Stack and
register
operations
Integer
and logic
operations
Program-
ming
Getting used to the groups, you will very soon find your functions on your WP 34S easily.
Most of the 168 labels printed on it point to operations carrying simply the same name.
, for instance, calls the function ALL and calls FIX. In the example above,
however, pressing called the function POL there are a few special labels like this.
Let us introduce them to you, starting top left on the keyboard:
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1. , , , and are named hotkeys calling directly the user programs carrying
these labels. Take your chance to make up to four of your favorite functions directly
accessible. Unless the respective labels are defined, these keys act as
, , , or , respectively, as is printed above them.
2. (i.e. + ) is the
prefix for hyperbolic functions
SINH, COSH, and TANH;
(i.e. + ) is the
prefix for their inverses ASINH,
ACOSH, and ATANH. Similar-
ly, stands for ASIN, etc.
3. is a prefix for direct con-
version of the value displayed
(i.e. x). It may be trailed by
, , , , or
(the respective function
names then read e.g. H.MS).
trailed by , , or
will display xconverted to an
integer of the respective base.
is also used for indirect
register access (see below).
converts polar to rect-
angular coordinates in a plane,
converts vice versa. So
this pair covers the two classic
coordinate transformations
(see REC and POL).
4. is for calling complex operations (see p. 29). and enter fraction
mode for proper or improper fractions (see PROFRC and IMPFRC).
5. and represent the classic two time modes, where the latter stands for
decimal hours and also for decimal floating point numbers in general (see DECM).
6. sets alpha mode (see p. 61)., while , , , or set integer modes for
calculating with binary, octal, decimal, or hexadecimal numbers (see p. 52).
7. returns the logarithm for base 10, does the same for base 2 .
8. calls x! in all numeric modes. and (calling COMB and PERM here)
work like on an HP-15C. calls CORR, calls ABS, and calls ROUND.
9. There are three toggles: for radix marks, for programming (like on an
HP-15C), and for upper and lower case in alpha mode.
These are all the special labels featured. A complete list of each and every command
provided on your WP 34S, the keystrokes calling it, and the necessary individual
explanation is in the Index of Operations (IOP) below for your reference.
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Let us return to our introductory example for two remarks8:
1. There is no need to enter units in your calculations. Just stay with a consistent set of
units and you will get meaningful results within this set.9If you want to convert results
from one unit to another, however, see the catalog CONV described further below.
2. Although we entered integer numbers only for both sides of our little ground, your
WP 34S calculated the diagonal in default floating point mode. This allows for
decimal fractions of e.g. yards in input and output as well. Another mode lets you
enter proper fractions such as e.g. 6 ¼ where you need them. Your WP 34S features
more modes we will introduce them to you from p. 35 on). Before, let us show you
some ways to enter numbers in your WP 34S and to further deal with them in typical
calculations .
Entering Numbers
is as easy as typing. For 12.34, for
example, press . Any digit
mistyped may be deleted immediately by
and entered correctly thereafter.
For negative numbers such as 5.6 , press
or or
the changes the sign of the number put
in.
For entering really big stuff such as the
age of the universe as we know it, do it this
way: resulting in 13.8
with nine digits trailing the point, i.e.
13 800 000 000 years. Really tiny numbers
such as the diameter of an atom
(0.000 000000 1mten zeroes heading
the 1) are entered in full analogy:
correspond -10 m.
Any numeric input will just fill the display and is interpreted when completed, not earlier.
8Generally, we assume you have graduated from US High School at minimum, passed Abitur, Matura, or an
equivalent graduation. So we will not explain basic mathematical rules and concepts here.
And in four decades of scientific pocket calculators, a wealth of funny to sophisticated sample applications
has been created and described by different authors more and better than we can ever invent ourselves.
It is not our intention to copy them. Instead, we recommend the DVD mentioned above once again:
it contains nearly all the user guides, handbooks, and manuals published for vintage Hewlett-Packard
calculators beginning with their very first, the HP-9100A of 1968. Be assured that almost every calculation
described there for any scientific calculator can be done significantly faster on your WP 34S and often
even in a more elegant way.
9 The big advantage of SI is that it is the largest consistent set available.
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Real Calculations
Most of the commands your WP 34S features are mathematical operations or functions
taking and returning real numbers such as 1 or -2.34 or or 5.6E-7. Note that integer
numbers such as 3, 10, or -1 are just a subset of real numbers.
Many real number functions provided operate on one number only. For example,
enter 0.49
and press . You will get 0.7 since 0.72= 0.49 .
Generally, such functions replace x(i.e. the value displayed) by its
result f(x). In this example, f(x).
The vast majority of calculators works this way, so this is no real surprise.
Some of the most popular mathematical functions, however, operate on two numbers
instead. Think of + and , for example.
Example: Assume having an account of 1,234 US$ and taking 56.7 US$ away from
it. What will remain? One easy way to solve such a task works as follows:
On a piece of paper
On your WP 34S
Write down the 1st number:
1234
Key in the 1st number:
1234
Start a new line.
Separate 1st from 2nd:
Write down the 2nd number:
56.7
Key in the 2nd number:
56.7
Subtract:
1177.3
Subtract:
1177.3
This is the essence of RPN:
Provide the necessary operands, then execute the requested operation.
And a major advantage of RPN compared to other entry systems for calculators is that it
sticks to this basic rule. Always.10
As the paper holds your operands before you calculate manually, a place holding your
operands on your WP 34S is required. The stack does that. It will also take care of
intermediate results, if applicable, as your paper may do. Turn overleaf to see how this is
done.
10 Some people claim this being true for RPLonly. RPL is a language developed from RPN
Maybe they are even right. In my opinion, however, RPL strains the underlying postfix principle beyond the
pain barrier, exceeding the limit where it becomes annoying for the human brain. Not for everybody, of
course, but also for many scientists and engineers. Thus we decided to stick to RPNon the WP 34S.
Edition 3.1
Page 17 of 211
Elementary Stack Mechanics
Think of the stack like a pile of registers11: bottom up,
they are traditionally named X, Y, Z, T, optionally
followed by A, B, C, and Don your WP 34S. New input is
always loaded in X, and only its content xis displayed.
separates two input numbers by closing the
number xand copying it into Y12, so Xcan take another
numeric input then without losing information.
After having completed the second numeric input in the
little account example above, subtracts xfrom yand
puts the result f(x,y)= yxinto Xfor display. This
method applies for most two-number real functions.
Stack register
content
D
d
C
c
B
b
A
a
T
t
Z
z
Y
y
Display
X
x
A large part of mathematics is covered by two-number functions of this kind, and
combinations of such operations. Let us look at a chain calculation, for example
.
This is as a combination of six two-number functions: two subtractions, an addition, a
product, an exponentiation, and a division. And this is how it is solved on your
WP 34S, starting top left, and what happens on the stack during the solution: 13
T
Z
Y
12.3
12.3
X
12.3
12.3
45.6
-33.3
Input
You will have recognized that the first parenthesis was solved exactly as shown in
our little account example above. Now proceed to the second parenthesis:
T
Z
-33.3
-33.3
Y
A-33.3
78.9
78.9
-33.3
X
78.9
78.9
1.2
80.1
-2,667.33
Input
11 Learn more about the registers provided by your WP 34S in next chapter.
12 This is the classic way ENTER worked from the HP-35 of 1972 until the HP-42S ceased in 1995. It is often
said ENTER x. In doing so, the higher stack contents are lifted out of the way before.
So zgoes into Tand yinto Zbefore xgoes into Y. See page 20 for detailed stack pictures.
The HP-30b employs a different ENTER the WP 34S sticks to classic RPN, however.
13 There may be data loaded in the higher stack levels already. They are from previous operations and are
not relevant for this calculation, so leave them aside here.
Edition 3.1
Page 18 of 211
Note the result of the first parenthesis was lifted automatically (A) to Yto avoid
overwriting it when the next number was keyed in step 1 of this row. This is called
automatic stack lift and is standard in RPN calculators.14
And after having solved the second parenthesis in step 4 of row 2, we had the results
of both upper parentheses on the stack so everything was ready for multiplication
to complete the numerator and we did it.
Now we will simply continue and start calculating the denominator:
T
Z
-2667.33
-2667.33
A-2667.33
Y
A-2667.33
3.4
3.4
-2667.33
A-2.2
-2667.33
X
3.4
3.4
5.6
-2.2
7
-249.43
Input
Last job remaining is the final division of numerator by denominator. Both are on the
stack in the right order. Just press and see the result: 10.6934534648 .
As you have observed several times now, the contents of the stack registers drop when a
two-number function is executed. Like the automatic stack lift mentioned above, this stack
drop affects all levels: xand yare combined giving the result f(x, y) loaded into X, then z
drops to Y, and tto Z. Since there is nothing available above for dropping, the top stack
level content will be repeated here. You may employ this top level repetition for some nice
tricks. See the following compound interest calculation, for example:
Assume the bank pays you 3.25% p.a. on an amount of 15,000 US$; what would be
your account status after 2, 3, 5, and 8 years? You are interested in currency values
only, so set the display format to 2 for this. It causes the output being shown
rounded to next cent (internally, the numbers are kept with far higher precision).15
T
1.0325
1.0325
1.0325
1.0325
1.0325
1.0325
Z
1.0325
1.0325
1.0325
1.0325
1.0325
1.0325
Y
1.0325
1.0325
1.0325
1.0325
1.0325
1.0325
X
1.0325
1.03
15 003
15990.84
16510.55
17601.17
19373.66
Input
1.0325
15 3
after 2
years
years
years
years
Here, each multiplication consumes xand yfor the new product put in X, followed by
zdropping to Y, and tto Z. Due to top level repetition the interest rate is kept as a
constant on the stack, so the accumulated capital value computation becomes a
simple series of strokes.
14 For a four level stack, the full automatic stack lift procedure is moving zto T, then yto Z, and finally xto Y.
The old content of the top level Tis overwritten. So automatic stack lift affects all stack levels. It will not be
indicated after this example anymore. In fact it is worth mentioning when automatic stack lift is disabled
since this is under fixed conditions only and occurs far rarer.
15 In the following, we will use plain text for numeric input for space reasons, unless mentioned otherwise.
Edition 3.1
Page 19 of 211
Debt calculations are significantly more complicated so avoid debts whenever
possible! In the long run, it is better for you and the economy. Nevertheless, you can
cope with those calculations using your WP 34S as well (see further below).
There are also a few three-number real functions featured by your WP 34S (e.g.
DATE and %MRR) replacing xby the result f(x, y, z). Then tdrops into Yand so on,
and the content of the top stack level is repeated twice.
Some real functions (e.g. DECOMP or DATE) operate on one number but return two or
three. Other operations (such as RCL or SUM) do not consume any stack input at all but
just return one or two numbers. Then these extra numbers will be pushed on the stack,
taking one level per real number.
In addition to the traditional stack and register control
operations , , , , , LASTx,
CLSTK, , , and known for decades
and mostly found within the blue frame on the
keyboard your WP 34S also features , DROP,
RCLS, STOS, SSIZE4, SSIZE8, SSIZE?, Y, Z,T,
and . Turn overleaf to learn what , ,
DROP, , , , and LASTx do with the stack
if SSIZE4 or SSIZE8 is set. See the IOPfor information
about the other commands.
For the first time ever in a calculator, your WP 34S offers you a choice of four or eight
stack levels (see SSIZE4 and SSIZE8). Thus, the fate of stack contents depends not only
on the particular operation executed and its domain but also on the stack size chosen.
Real functions in a four-level stack work as known for decades. In the larger stack of your
WP 34S everything works alike just with more levels for intermediate results. Turn
overleaf for details.
Edition 3.1
Page 20 of 211
Level
Assumed
stack contents
at the
beginning:
Stack contents after
stack register operations
number
such as x2
numbers
such as /
ENTER
FILL
DROP
xy
R
R
LASTx
With 4
stack
levels
T
t = 44.4
33.3
11.1
44.4
44.4
11.1
33.3
33.3
44.4
44.4
Z
z = 33.3
22.2
11.1
44.4
33.3
44.4
22.2
22.2
33.3
44.4
Y
y = 22.2
11.1
11.1
33.3
11.1
33.3
11.1
11.1
22.2
33.3
X
x = 11.1
11.1
11.1
22.2
22.2
22.2
44.4
last x
123.21
2
With 8
stack
levels
D
d = 88.8
77.7
11.1
88.8
88.8
11.1
77.7
77.7
88.8
88.8
C
c = 77.7
66.6
11.1
88.8
77.7
88.8
66.6
66.6
77.7
88.8
B
b = 66.6
55.5
11.1
77.7
66.6
77.7
55.5
55.5
66.6
77.7
A
a = 55.5
44.4
11.1
66.6
55.5
66.6
44.4
44.4
55.5
66.6
T
t = 44.4
33.3
11.1
55.5
44.4
55.5
33.3
33.3
44.4
55.5
Z
z = 33.3
22.2
11.1
44.4
33.3
44.4
22.2
22.2
33.3
44.4
Y
y = 22.2
11.1
11.1
33.3
11.1
33.3
11.1
11.1
22.2
33.3
X
x = 11.1
11.1
11.1
22.2
22.2
22.2
88.8
last x
123.21
2
Using the stack, RPN makes all parentheses such as , , , , , or completely unnecessary in calculations. There is no
operator precedence. Here is another example showing a slightly more complicated formula and the keystrokes used for solving it:
7 4 5 6
6.5 5.9 3 7 1.7
3.5
7.6 .8 30 7 4
6 5 5.1
.3 1
complete denominator
complete numerator
complete result (0.37)
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