HP 42S, Free42 User Manual
An Alternative HP-42S/Free42 Manual
Version 0.7 ─ January 2010
Author: José Lauro Strapasson, Brazil
jlstrapasson@uol.com.br http://joselauro.com/42s.pdf
With contributions by Russ Jones, Manhattan Beach, California
Copyright (C) 2010 José Lauro Strapasson.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU
Free Documentation License, Version 1.3 or any later version published by the Free Software
Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of
the license is included in the section entitled "GNU Free Documentation License".
For more information visit the Free Software Foundation at
http://www.fsf.org
Contents
1 Introduction..........................................................................................................................................3
2 Basic Operations ..................................................................................................................................4
2.1 RPN...............................................................................................................................................4
2.2 Turn ON/OFF................................................................................................................................5
2.3 Setting the display contrast ........................................................................................................... 5
2.4 Training RPN using HP-42S.........................................................................................................5
2.5 Menus............................................................................................................................................5
2.6 DISP Menu....................................................................................................................................6
2.6.1 The FIX function....................................................................................................................6
2.6.2 The ALL function .................................................................................................................. 6
2.6.3 The SCI function....................................................................................................................6
2.6.4 The ENG function..................................................................................................................6
2.6.5 RDX. And RDX, functions....................................................................................................7
2.7 MODES Menu .............................................................................................................................. 7
2.8 The Stack ......................................................................................................................................7
2.9 Getting used to some keys of the keyboard ..................................................................................8
3 Memory..............................................................................................................................................10
3.1 The CATALOG menu............................................................................................................11
3.2 More on the CLEAR menu..................................................................................................... 11
3.3 The CUSTOM menu ..............................................................................................................12
4 Probability..........................................................................................................................................12
5 Complex Numbers .............................................................................................................................13
5.1 Complex numbers in rectangular coordinates.............................................................................13
5.2 Complex numbers in polar coordinates ......................................................................................14
6 Programming......................................................................................................................................14
6.1 Basic programming.....................................................................................................................14
6.2 More than one program in the memory.......................................................................................16
6.3 The X?0 and X?Y sub-menus .....................................................................................................17
6.4 Real program examples...............................................................................................................18
7 Using the Solver.................................................................................................................................19
8 Numeric Integration...........................................................................................................................20
9 Statistics .............................................................................................................................................21
9.1 The sub-menu CFIT....................................................................................................................22
9.2 The second line: ALLΣ, LINΣ, ΣREG and ΣRG? Functions...................................................... 22
10 Matrices ...........................................................................................................................................23
11 Other Bases ......................................................................................................................................26
12 Flags.................................................................................................................................................26
13. Free42-Specific Features ................................................................................................................27
13.1 Keyboard Interface (Windows, Linux and Mac Desktops and Laptops)..................................27
13.2 Program Import and Export ...................................................................................................... 28
13.3 Printing......................................................................................................................................28
14. Comprehensive Command List.......................................................................................................28
GNU Free Documentation License.......................................................................................................35
1 Introduction
Since HP-42S was a very nice calculator, and its official manual is no longer freely available and
there were many people looking for its manual, seemed good to me to write my own HP-42S manual.
I personally don't have a HP-42S (more than US$300 on ebay). I have a HP-33S and had a HP-48G,
but my brother has one and I also use Free42 simulator for PalmOS.
This manual will be of interest to people who:
a) Have a HP-42S calculator and lost its manual.
b) Got the Free42 simulator and want to know how to use it.
c) Have a palmtop with PalmOS and want a nice scientific calculator (get Free42)
d) Just want to have an idea how 42S was.
e) Have the official manual but don't want to read more than 300 pages!
Why HP-42S? Because it was a very, very nice calculator and also a powerful one. I know some other
HP models from the past and the present like 48G, 49G, 28S, 33S, 20S, 6S Solar, 15C, and even a TI36X Solar, etc, but 42S is my favorite. And because there is a free simulator (Free42) that works on
Palm OS, Windows and Linux and there are also some emulators (at the moment emulators are only
useful for who has a real calculator since HP-42S roms are not freely available). This calculator
played an unique position among HP calculators! Being a scientific programmable 100% RPN
calculator, it also had some graphing abilities but was pocketed sized and non RPL (some people as
me like RPN, but dislike RPL).
It is important to say that this manual is not complete and I don't want it to be. Two things I really
don't want to see here are PRINTING and HP-41 compatibility. This because I suppose most owners
don't have the printer (and it is not so useful) and also haven't had a HP-41 prior to HP-42S.
If you want to download the fantastic Thomas Okken Free42 program please go to this web site
http://home.planet.nl/~demun000/thomas_projects/free42/
In my opinion Free42 is even better than the real HP-42S. Try asin(acos(atan(tan(cos(sin(6°)))))).
For more information about HP-42S please see
http://www.hp42s.com http://www.hpmuseum.org/hp42s.htm
Here you can find emulators for HP-42S http://privat.swol.de/ChristophGiesselink (very nice)
http://www.geocities.com/hrastprogrammer/HP42X/index.htm
I would like to finish this introduction saying that it would be nice to have the HP-42S back to life
again and even better to have a model (both real and in simulator/emulator form) based on HP-42S
but with some of the 33S features like more memory, an equation editor, fractions, program lines
starting with letters, physical constants, units conversion, less useless functions, etc. And it also would
be nice to have HP-42S ROM images for free just like what happened to HP-48G and other models
and keeping PDF versions of the manuals of retired models to download would be nice too. Perhaps
someone will listen to me! ☺
A quick note on notation: throughout this manual, for the most part, keys that are to be pressed are
denoted by putting them in a box, e.g. ENTER, except when the keys are numbers or arithmetic
operators. Keys that are “2nd functions” denoted by orange lettering on the calculator are denoted in
orange with an orange box preceding it, e.g. ALPHA.. Functions that are accessed through the
menus are generally denoted by shading in grey, such as in FCN.
2 Basic Operations
2.1 RPN
The HP-42S, like most old HP calculators, is a RPN calculator. RPN comes from “Reverse Polish
Notation”. In RPN we first enter data and then we enter the mathematical operations.
Example: To make a simple operation like 2+2 in a normal algebraic calculator we do “2 + 2 =”
which give to us 4. To make this same calculation using a RPN calculator we do “2 ENTER 2 +”
As we can see in RPN mode we first enter the data pressing the ENTER key after every data (except
for the last in HP's RPN) and then we enter the operations.
Let’s now consider the following calculation
4 + (2 × 79)
In a RPN calculator we do
2 ENTER 79 × 4 +
But how could one do this in an algebraic calculator? If the calculator has “(“ and “)” keys we enter
4 + ( 2 × 79 ) =
But if there are no parenthesis keys we might do this in a good calculator by doing
4 + 2 × 79 =
By a “good” calculator we mean a calculator which knows that “×” and “/” have precedence over “+”
and “–“. In a bad algebraic calculator which does not know this we have to do
2 × 79 =
and
+ 4 =
Or
2 × 79 + 4 =
What about to calculate sin(33°)? In a RPN calculator we enter
33 sin
or if you prefer
33 ENTER sin
(in this case we don't need to press enter key)
But in an algebraic calculator we have two ways. In the classic old models it is like RPN and we do
33 sin
but in some modern models (which typically allow you to edit entered data using cursors) we do
sin 33 =
So algebraic calculators are ambiguous because the many ways they work. RPN calculators are more
standard and so less ambiguous. The main key to understand how to use RPN in more complex
calculus is to realize that in RPN we make calculations from “inside” to “outside” instead of from left
to right. For example:
8 × ln [5+sin(40°)]
in RPN this is accomplished by
40 sin 5 + ln 8 ×
In RPN calculators, there is no operator precedence — operators are executed immediately and the
order of the calculations determines precedence. There is never any need for parentheses. In RPN we
can make any calculation we could do in algebraic devices and this is not only more elegant but also
more effective since there are less ambiguities and we use less key strokes. For example, my HP-33S,
which is both algebraic and RPN, is always in RPN mode. (Just to insert equations I think algebraic
mode is better) For more information on RPN, please see
http://www.hpmuseum.org/rpn.htm
2.2 Turn ON/OFF
To turn your HP-42 on press ON. The ON key is the same EXIT key. To turn your HP-42S off press
OFF. OFF is in the same key as EXIT and ON, and by OFF we mean you have to press the
orange key before pressing the EXIT key (which has “OFF” in orange above it). The orange key is
what in some other calculators is called “second function”. When you press this all keys turn into
what is written in orange above them.
Actually OFF is a redundancy since OFF can be only accessed by pressing first. But (as in the
HP-42S official manual) we will do this just to remember when we have to press or not. If you
press this key a second time all keys go back to the normal function.
2.3 Setting the display contrast
HP-42S, as most HP calculators, can set the display contrast by pressing at the same time ON and +-
or – .
2.4 Training RPN using HP-42S
Now that you have your 42S on try to do the following calculations:
Calculation Keystrokes
6 × (4 + 3) 4 ENTER 3 + 6 ×
6 +{8×[2+(4/3)]} 4 ENTER 3 / 2 + 8 × 6 +
IMPORTANT: For sake of simplicity sometimes we will use / instead of ÷.
2.5 Menus
Not all functions of HP-42S are visible above the keys. It has menus with access to many more
functions. The menus are
ALPHA MODES DISP CLEAR
SOLVER ∫f(x) MATRIX STAT
BASE CONVERT FLAGS PROB
CUSTOM PGM.FCN PRINT TOP.FCN
CATALOG
2.6 DISP Menu
The DISP menu is the first menu we have to see. It is above E key. So start by pressing DISP.
When you do this the DISP menu appears in the first line with the following functions.
FIX SCI ENG ALL RDX. RDX,
These functions appear just above the top row of keys ∑+, 1/x, √x, LOG, LN and XEQ. Now with
the DISP menu active those keys don't represent their original functions but those of the DISP menu.
The same happens with all menus.
2.6.1 The FIX function
The FIX “function” is not a function in the mathematical sense, but a calculator function. By
usingFIX function the display becomes with a fixed number of digits after decimal point. Ok, press
FIX. (I mean ∑+ with DISP menu active)When you do this what appears isFIX _ _Then you have to
enter a number up to 11. For example FIX 0 4 sets the calculator to have 4 digits of precision after the
decimal point. A number like π will appear as 3.1416 and √2 will appear as 1.4142.(You can verify
this by doing π and 2 √x respectively)
If you put FIX 0 9 than those numbers will appear as 3.141592654 and 1.414213562. It is important
to say that this is not the actual precision the calculator will have but just the display precision. To see
all calculator precision you have to press ALL in DISP menu (above LOG key). By doing so those
numbers will appear as 3.14159265359 and 1.41421356237. As you can see the numbers are not
truncated but rounded.
Not all numbers can be seem with a fixed decimal precision. If you put 4 digits for fixed precision the
number π will appear as 3.1416 but if one calculates 10
8
(do this by doing 8 10x or by entering 1E8)
what you are going to see is 100,000,000.000 with 3 decimal digits. This happens because the
calculator cannot show more than 12 digits at a same line.
2.6.2 The ALL function
We already talked about the ALL function. It makes the calculator to show all of its precision.
2.6.3 The SCI function
The SCI function works just like FIX one but puts the calculator in “scientific” mode. The numbers
will be shown as a decimal number between 1 and 10 times a power of 10. For example 1000 will be
represented as 1.00E3 with you put the calculator in scientific mode with 2 digits. 1.00E3 means
1.00×10
3
. The π number will appear as 3.14E0.
Actually even when in FIX mode, the calculator will convert some answers to scientific notation. For
example if you calculate 1.0001-1 with FIX 3 you are not going to get 0.000 but 1.000E-4. This
means that the calculator is “smart” and shows the result in the best way as possible.
Exercise. Show that 1.0001 – 1 gives 1.000E-4 in FIX 3 mode.
Answer: First we put the calculator in FIX 3 mode by doing DISP FIX 0 3.
Then we do 1.0001 ENTER 1 – and we get the answer.
As you can see, when you are in FIX mode a sign ■ appears on the right side of the FIX name in the
DISP menu. This means FIX mode is active. The same happens with SCI, ALL, etc.
2.6.4 The ENG function
The ENG function puts the calculator in engineering notation. It looks like scientific notation but now
the first number does not need to be between 0 and 1 but can be between 0 and 1000 and the power
will be always 3 manifold (corresponding to the magnitude prefixes such as milli-, micro-, kilo-,
mega-, etc. used in engineering units). For example: 100 will be represented by 100.E0 in ENG 2
mode while 1000 will be 1.00E3 in the same mode. Why do we get 100.E0 for 100 instead of
100.00E2 in ENG 2 mode? Because the calculator shows in engineering mode the same number of
digits it shows in scientific mode.
2.6.5 RDX. And RDX, functions
In some countries like Brazil we use ',' for the decimal point instead of '.' and also '.' instead of ',' for
thousands separators. For example π is written here (Brazil) as 3,141 etc and not as 3.141 etc. In FIX
3 mode one million is written here as 1.000.000,000 and not as 1,000,000.000 as in English use. By
pressing RDX, you make the calculator to use ',' for the decimal point and by pressing RDX. we make
it use '.' for decimal point. Again the active mode is followed by a ■ sign. Here, in this manual, I
assume the calculator is using '.' for decimal point.
2.7 MODES Menu
To access MODES menu just press MODES. (MODES is above +/– key).
DEG actives degree mode for trigonometric functions. In this mode a circumference has 360°. RAD
actives radian mode and in this mode a circumference has 2π radians or just 2π.GRAD is not so
useful and correspond to 400 degrains for a circumference. For example: In degrees we have
sin(90°)=1 and in radians we have sin(π/2)=1.
Try this: π 2 / COS in radians mode. Why the result is not exactly zero?
Answer: Because the number that calculator entered was not exactly π but 3.14159265359.
REC actives rectangular mode (x,y) and POLAR actives polar mode (r,θ). We will see this more in
detail when study complex numbers.
The MODES menu has another line but we will discuss this later. We will discuss the others menus
later too.
2.8 The Stack
The stack is intimately related to the way the calculator uses RPN to perform calculations so it’s a
good idea to understand the concept and behavior of the stack. On the HP42S, the stack consists of 4
registers named X, y, z and t, and normally the values of x and y (or just x if a menu is active) are
displayed.
No calculator can store an infinite amount of data. In algebraic calculators the “( )” are limited to a
given number depending on the model. The same happens in RPN calculators. In some models like
HP-48 or HP-49 the amount of input data is limited only by available memory. But in other models
like 32SII, 33S (in RPN mode) and 42S the input data have to fit in a “stack” of four lines. There are
four lines labeled x, y, z and t. So the stack is something like
t: 0.0000
z: 0.0000
y: 0.0000
x: 0.0000
But since the calculator’s display has only two lines just x and y lines are visible. When you enter a
number (say 2 ENTER) what happens is the following.
i) The content of lines t and z are lost.
ii) The content of line y goes to line t.
iii)The content of line x goes to line z.
iv)The content just entered goes to line y and line x.
So what you just entered appears twice. So if you do 2 ENTER + you will have 4 as answer.
This is a feature, a bad feature I think, of the HP RPN style used by the 42S (also in the 33S, 12C, etc
but not in the HP48 or 49). In my opinion we could have a simpler RPN style. Anyway there is
another way to enter data in RPN, namely yo just type the number and then press the desired function
key. For example, if you do 2 1/x , the calculator makes an automatic ENTER before the 1/x function
but in this case the content just entered appears only once. So if you do 2 1/x or another example 9 √x
what you will have will be
i) Only the content of the t register will be lost.
ii) The content of the z register goes into the t register.
iii) The content of y goes into z.
iv) The content of x goes into y.
v) Your result will be in the x register.
This second way to enter data looks more intuitive to me and I think it should be always like this. But
it is not!:( So to do 2+3 we have to do2 ENTER 3 + (and not 2 ENTER 3 ENTER +).(Actually one
can also use EXIT to enter a number without duplication). If you just press ENTER you duplicate
what is in register x. When making a calculation one should never forget about the limitation of the 4
lines of the stack. The lines of the stack cannot contain only numbers but also matrices, complex
numbers, etc.
Two basic operations with the stack are: x<>y and R↓. The first exchanges the value in register x
with the value in register y. The second makes the stack “roll down” (t goes to z, z goes to y, y goes to
x, and x rolls around to t).
In the CLEAR Menu there are some interesting functions: CLST which clears all the stack(something
missing in HP-33S). CLX clears the line x in the same way of pressing ← . The ← is more used to
correct a number when typing it. Another useful function is LASTx which gives the last calculated
result.
2.9 Getting used to some keys of the keyboard
Let's discuss some basic keys of the calculator. We will start from upper left side. Σ+ and Σ-: These
are statistical functions. We will discuss this later.
1/x and yx The 1/x key just calculates the inverse of a number which is in register x. yx is the
potential function. To calculate 5 3 = 5×5×5 we do 5 ENTER 3 y x.
√x and x
2
: These functions just calculate the square root and the square of a number in x. When
studying complex numbers we will see that unlike the HP-33S, in HP-42S the number in
square root can be negative.
LOG and 10 x: These functions calculate the base 10 logarithm and its inverse.
LN and e
x
: These functions calculate the natural (base e=2.71828...) logarithm and its inverse. If
we want a logarithm in another base, we can use the relation logz y=logz y / logz x where z is
any other base. If we take z = e = 2.71828 then we have log
x
y=ln y / ln x .
Example: Calculate log2 8
Answer: 8 LN 2 LN / which give us 3 because 23 = 8.
XEQ and GTO: These are related to programming and we shall discuss this later. XEQ will also be
discussed in ALPHA menu part.
STO and COMPLEX : These are related to the memories and complex numbers. We will discuss
this later.
RCL and % : RCL is related to memories and we will discuss later. % is the percentage
function. To calculate 10% of 300 we do 300 ENTER 10 % which gives 30 as the answer.
Note that 300 remains in line y, so if you want to calculate 300 plus 10% you do 300 ENTER
10 % +
R↓ and π : We already discussed these. The first “rolls down” the stack and the other returns
π=3.14...
SIN and ASIN : These are the sine trigonometric function and inverse. The angle type is set up as
said before in the MODES menu. The default is degrees. ASIN is the inverse usually called
arcsine or sometimes sin
–1
(not to be confused with cosecant which is 1/sin). It is important to
remember that ASIN is not a real function since there is no single result. For example
sin(135°)=sin(45°)=√2/2 but the calculator gives always ASIN(√2/2)=45°. HP-42S will give a
complex number if the input of an arcsinus is bigger than 1 or smaller than -1.
COS and ACOS: These are the cosine trigonometric function and inverse.
TAN and ATAN: These are the tangent trigonometric function and inverse. Not all numbers can
have a result for tangent. For example tan(90°) goes to infinity. The HP-42S gives a big
number instead.
ENTER and ALPHA: The ENTER key does not need any comment. ALPHA is the alpha-
numeric menu used to enter letters instead of numbers. When you press ALPHA what
appears is
ABCDE FGHI JKLM NOPQ RSTUV WXYZ
These are sub-menus. If you press now ABCDE what you will have is
A B C D E
Then just pick the letter you want. But above you can see this symbol
▼▲. This symbol means
the menu has more than on line. You can access the other lines by pressing ▲ or ▼. In this
case there is just one more line with Ă, Å and Æ. If you press FGHI you will have F G H I,
etc. Among all calculators I know this is in my opinion the best way to enter letters! The main
ALPHA menu also has a
▼▲ symbol. The other line has the following submenus.
( [ { ← ↑ ↓ < = > MATH PUNC MISC
Much more than one will ever need! If you are inside a submenu and want to go back to the
main menu just press EXIT. Why is the ALPHA menu useful? Of course it is useful to label
programs and data in memory, but it is also useful to enter commands using the XEQ key!
For example XEQ “SIN” is the same of pressing the SIN key. The “” are called automatically
when pressing ALPHA and ENTER. XEQ “SINH” calculates the hyperbolic sine while
XEQ “OFF” turns the calculator off. Finally we must say that ALPHA is not always
needed! In some cases like XEQ and GTO (we will see this later) a simple ENTER will do.
Entering alphabetic text is even easier with Free42. Free42 allows you to just type on the
native keyboard when the ALPHA menu is activated.
x<>y and LASTx: We already talked about these.
+/–: This just changes the sign of a number.
E and DISP: We already talked about DISP menu. The E is the character meaning the power of 10
in scientific notation. For example, to enter 5.2x 1022 we do 5.2 E 22 ENTER.
← and CLEAR: As said before, ← clears line x and if you are entering a number you can delete
the last character. We already talked a little about CLEAR menu and we will discuss it again
later.
▲ or ▼: As said before we use this to change the line in a multi line menu. We will see BST and
SST later.
The keys from 0 to 9 have obvious functions.
. and SHOW: The '.' is just the decimal point and SHOW is used to show a number for an
instant with all precision. For example: If you have π in the first line and you are using the
display in FIX 4 you have 3.1416 but pressing SHOW you will see 3.14159265359 for an
instant.
3 Memory
The real HP-42S has about 7200 bytes of memory while Free42 can have much more depending on
the available memory in the computer/handheld. In fact, 7200 bytes is a lot of memory for the HP42S! A program of 10 lines uses about 15 bytes of memory. This means that, while in some other
models like the HP-20S you would be able to program just 99 lines, with 42S you would be able to
create programs with thousands of lines!
This available memory is shared with everything including programs, variables, etc. Let's start from
the basic. To store a number which is in register x of the stack we use the STO function. The HP-42S
has by default 25 positions in the memory from R
00
to R24. To store the number π in R10 just do the
following: π STO 10 To get it back it is just do this: RCL 10.
If you want to make an operation you can use STO+, STO–, STO×, STO÷. Any of these operations
can be entered by pressing the STO key followed by the operator key, followed by a register number
or name. For example, 6 STO – 05 subtracts 6 from the number in R
05
. 2 STO ÷ 10 divides the
number in R10 by 2.You can also use RCL+. RCL–, RCL×, RCL÷, but it is not so fun. This gives the
result of the calculation but does not change the number in the memory.
If 25 positions in the memory is not enough for you, you can change this number by using the SIZE
function (which is in the second line of the MODES menu). For example MODES ▼ SIZE 0100
changes to have 100 positions, from R00 to R99. Although it is possible, I suggest you should not use
more than 100 positions. These positions are stored in a normal matrix called REGS (we, the poor
owners of the HP-33S for example, just have 26 memory positions, from A to Z).
But this kind of memory position only accept real numbers! What about if you want to store other
things? Matrices, complex numbers of even other real numbers? To do this HP-42S has an arbitrary
number of positions, limited only by the memory available, which use letters to label the positions
instead of numbers. We had stored the π number in R
10
but we can create a variable called, for
example ,“PI” to store it. To do so we just do π ENTER STO ALPHA “PI” ENTER.
Actually is not just PI you type but NOPQ P FGHI I but we wrote that for simplicity. Now to
get this number back it is just type RCL “PI”. When you type RCL the “PI” should appear for you to
select it. More generally, the STO and RCL functions automatically bring up a menu of previously
defined varables currently active in the calculator, and you can use the arrow keys if there are more
than will fit on one screen.
You can also use STO+, STO–, STO× and STO÷ even in this case since the types of the things you
are operating are the same.
We can deal with the four registers of the stack as we deal with the memory positions. In this case the
lines of the stack are called ST X, ST Y, ST Z and ST T respectively. To access this we press '.'
before the name of the register. For example: 5 STO . ST X puts 5 in line x of the stack. The
submenu that is displayed when we press ‘.’ Actually has two other items, ST L and IND. ST L refers
to the LASTx register, and IND is used for indirect parameters.
As the content of the stack can change easily I don't think “STO .” is a good thing. But I cannot say
the same of “RCL .” which may be very useful to get the content especially of registers z and t. You
can also use STO and RCL with +, -, x and ÷ and '.' to work with the content of the registers of the
stack. For example:5 STO ÷ . ST Z divides register z by 5.
We can use an indirect parameter by pressing . IND when using STO or RCL or any other
calculator function that happens to allow indirect parameters. With indirect addressing, we specify a
location where the actual parameter is stored, rather than the parameter itself. That location could be
a named variable, one of the numbered storage registers, or a stack register. For example, to assign
the value 125 to the register specified in the variable ABC:
10 STO “ABC” sets variable ABC to the value 10
125 STO . IND “ABC” stores 125 in the register pointed to indirectly by “ABC”
RCL 10 returns the value 125 to the x-register
3.1 The CATALOG menu
The CATALOG menu has the following submenus:
FCN PGM REAL CPX MAT MEM
FCN: It shows all the functions available in HP-42S calculator. It has many lines and one must use the
▼ and ▲ to navigate through the lines. Here you are going to find important functions we
don't see in the keyboard including hyperbolic functions (SINH, COSH, etc), functions to
work with integer and real numbers like IP (integer part) and FP (fraction part), programming
functions, etc. Don't forget you can also use XEQ “function name”.
PGM: It shows all variables with programs in the memory.
REAL: It shows all variables with real numbers in the memory. (But does not show numbers in the
numbered registers R
00
, etc)
CPX: It shows all variables with complex numbers.
MAT: It shows all variables with matrices. The REGS matrix always appears. It contains the numeric
memories R
00, R01, etc.
MEM: It shows all available memory.
3.2 More on the CLEAR menu
We already saw some of the CLEAR menu functions, but there are also:
CLV: Clears variables we had stored using STO “name”.
CLRG: Clears the R00, R01, … memories known as registers.
CLLCD: Clears the LCD display (may be useful when plotting)
CLALL: Clears all the memory of the calculator.
3.3 The CUSTOM menu
This is not really related to memory, but as we have just discovered the FCN menu within the
CATALOG menu, now is a convenient place to talk about it.
The HP-42S calculator has a lot of functions. So many, in fact, that it is inconvenient to find the
function you want every time in the FCN menu or to use XEQ “function name” every time. To solve
this problem HP-42S has the CUSTOM menu which can contain functions or user-written programs
you personally select. To do this we use ASSIGN. When you call this you can select a function
from FCN and also some other things. For now we are interested in functions so press FCN. Now you
find the function you want and then you press the position you want it to appear in the CUSTOM
menu.
Example: Let's put ABS (absolute value) in the first position of CUSTOM menu.
ASSIGN FCN ABS
In the display you are going to see:
ASSIGN “ABS” TO _
Then you pick a position, for example initially the CUSTOM menu is empty and you have
___ ___ ___ ___ ___ ___
and you press the first ___ your CUSTOM menu will become
ABS ___ ___ ___ ___ ___
As you can see the CUSTOM menu has also the
▼▲ symbol which means there are more than one
line. There are three lines you can use when calling ASSIGN function which means 18 available
positions.
(I would like to use this space to make a complaint) There are some HP models with more than 2000
functions! Many functions does not always mean power but does always mean complexity!
4 Probability
Probability functions are in PROB menu (over the × key). They are COMB, PERM, N!, GAM,
RAN and SEED.
COMB: This calculates the number of combinations of N things taken r at a time (mathematically
notated as C
r
N
). The order does not matter. A thing cannot appear more than one time.
Example: If we have the five letters a, e, i, o and u the possible combinations taken one at a
time are {a,e,i,o,u} or 5 combinations.
Taken two at a time:{ae, ai, ao, au, ei, eo, eu, io, iu, ou} or 10 combinations.
Taken four at a time {aeio, aeiu, aeou, aiou, eiou} or 5 combinations.
The number of combinations C is given by
)!(!
!
rNr
N
C
N
r
−
=
where N! = N×((N–1)×(N–2)× … × 2 × 1. To calculate this using 42S just enter N, press
ENTER, enter r and press PROB COMB.
PERM: This calculates the number of permutations of N things taken r at a time (mathematically
notated as P
r
N
). A thing cannot appear more than one time but now the order matters.
Example: Five cars are in a race. Their colors are red, blue, green, white and cyan. What are
the possible results for the first, second, and third place winners?
Solution: For the first position we have five possibilities. For the second position we have
four possibilities, and three possibilities for the third position. So we have 5x4x3=60 different
arrangements. To see this using 42S just enter 5, press ENTER, enter 3 and press PROB
PERM. It is simple to realize that the number of permutations is given by
)!(
!rNN
P
N
r
−
=
In particular if r = N (all the things are taken) then the number of permutation is N!.
Example: In how many ways we can re-arrange the letters of the word “love”.
Solution: 4!=24.
N!: This just calculates the factorial of N given by N!=N.(N-1)...1 for a number (non-negative
integer). The biggest number allowed is HP-42S is 253 and in Free42 is 170.
GAM: This is the Gamma function which is defined by
∫
∞
−
=Γ
0
1
)( dxexa
xa
For a integer number we have Γ(n)=(n–1)! and Γ(n+1)=n! but the argument of the gamma
function can be a non-integer (but must be real). In this point HP-42S is different from the
33S which has only one function for both things.
RAN: This is the random number generator which gives a pseudo-random number in 0 ≤ x ≤ 1.
SEED: A sequence of pseudo-random numbers always starts with a seed. If you repeat the seed the
sequence repeats. To enter a new seed just enter a number and press SEED. If the seed is zero
the calculator will generate another seed.
5 Complex Numbers
5.1 Complex numbers in rectangular coordinates.
Unlike the HP-33S (and its ancestor HP-32SII) complex numbers are straightforwardly supported and
used in the HP-42S. There is almost nothing special to say. Just enter –1 and press √x, what are you
going to have is x: 0.0000 i1.0000 which means i. (Just for comparison, to do the same in HP-33S we
have to do 0 ENTER 1 +/– ENTER 0 ENTER .5 CMPLX y
x
and we will have 0 and 1 meaning i)
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