HP HP-42S User manual

An alternative HP-42S/Free42 Manual
(Version 0.6)
2005
Author: José Lauro Strapasson, Brazil.
[email protected]
http://joselauro.com/42s.p f

Inde
In ex
1 Intro uction
2 Basic Operations
3 Memory
4 Probability
5 Complex numbers
6 Programming
7 Using the Solver
8 Numeric Integration
9 Statistics
10 Matrices
11 Other Bases
12 Flags
License for this manual

1 Introduction
Since HP-42S was a very nice calculator, an its official manual is no longer freely available an
there were many people looking for its manual, seeme goo to me to write my own HP-42S
manual. I personally on't have a HP-42S (more than U$300 on ebay). I have a HP-33S an ha a
HP-48G, but my brother has one an I also use Free42 simulator for PalmOS.
This manual can interest people who:
a) Have a HP-42S calculator an lost its manual.
b) Got the Free42 simulator an want to know how to use.
c) Have a palmtop with PalmOS an want a nice scientific calculator (get Free42)
) Just want to have an i ea how 42S was.
e) Have the official manual but on't want to rea more than 300 pages!
Why HP-42S? Because it was a very, very nice calculator an also a powerful one. I know some
other HP mo els from the past an the present like 48G, 49G, 28S, 33S, 20S, 6S Solar, 15C, an
even a TI-36X Solar, etc, but 42S is my favorite. An because there is a free simulator (Free42) that
works on Palm OS, Win ows an Linux an 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 playe an unique position among HP calculators! Being a scientific programmable
100% RPN calculator, it also ha some graphing abilities but was pockete size an non RPL
(some people as me like RPN, but islike RPL).
It is important to say that this manual is not complete an I on't want it to be. Two things I really
on't want to see here are PRINTING an HP-41 compatibility. This because I suppose most owners
on't have the printer (an it is not so useful) an also haven't ha a HP-41 prior to HP-42S.
If you want to ownloa the fantastic Thomas Okken Free42 program please go to this web site
http://home.planet.nl/~ emun000/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 fin emulators for HP-42S
http://privat.swol. e/ChristophGiesselink (very nice)
http://www.geocities.com/hrastprogrammer/HP42X/in ex.htm
I woul like to finish this intro uction saying that woul be nice to have HP-42S back to life again
an even better to have a mo el (both real an in simulator/emulator form) base on HP-42S but
with some of the 33S features like more memory an equation e itor, fractions, program lines
starting with letters, physical constants, units conversion, less useless functions, etc. An also woul
be nice to have HP-42S roms for free just like what happene to HP-48G an other mo els an
keeping PDF versions of the manuals of retire mo els to ownloa woul be nice too. Perhaps
someone listen to me! :)

2 Basic Operations
2.1 RPN
HP-42S as most ol HP calculators was a RPN calculator. RPN comes from “Reverse Polish
Notation”. In RPN we first enter ata an then we enter the mathematical operations.
Example: To make a simple operation like 2+2 in a normal algebraic calculator we o
2 + 2 =
which give to us 4.
To make this using a RPN calculator we o
2 ENTER 2 +
As we can see in RPN mo e we first enter the ata pressing the ENTER key after every ata (except
for the last in HP's RPN) an then we enter the operations.
Lets now consi er the following calculation
4+(2x79).
In a RPN calculator we o
2 ENTER 79 x 4 +
But how one coul o this in an algebraic calculator?
If the calculator has the ( an ) sings it is just o
4 + ( 2 x 79 ) =
But if there are no () we o this in a goo calculator by oing
4 + 2 x 79 =
By a goo calculator we mean a calculator which knows that x an / are prior to + an -.
In a ba algebraic calculator which oes not know this we have to o
2 x 79 =
an
4 + =
or
2 x 79 + 4 =
What about calculate sin(33)? In a RPN calculator it is just o
33 sin
or if you prefer
33 ENTER sin
(in this case we on't nee to press enter key)
But in an algebraic calculator we have two ways.
In the classic ol mo els it is like RPN an we o
33 sin
but in some mo ern mo els (which typically allow you to e it entere ata using cursors) we o
sin 33 =

So algebraic calculators are ambiguous because the many ways they work. RPN calculators are
more stan ar an so less ambiguous.
The main key to un erstan how to use RPN in more complex calculus is to realize that in RPN we
make calculations from “insi e” to “outsi e” instea of from left to right.
Example:
8 x ln[5+sin(40)] in RPN is oing by
40 sin 5 + ln 8 x
In RPN we can make any calculation we o in algebraic evices an this is not only more elegant
but also more effective since there are less ambiguity's an we use less key strokes.
For example, my HP-33S, which is both algebraic an RPN, is always in RPN mo e. (Just to insert
equations I think algebraic mo e 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 of EXIT an ON, an by ▀ OFF we
mean you have to press the orange key before press the EXIT key which have OFF in orange above.
The orange ▀ key is what in some other calculators is calle “secon function”. When you press this
all keys turn in what is written in orange above it.
Actually ▀ OFF is a re un ancy since OFF can be only accesse by pressing ▀ first. But (as in HP-
42S official manual) we will o this just to remember when we have to press ▀ or not. If you press
this key a secon time all keys go back to the normal function.
2.3 Setting the display contrast
HP-42S, as most HP calculators, can set the isplay contrast by pressing at the same time ON an +
or -.
2.4 Training RPN using HP-42S
Now that you have your 42S on try to o the following calculations:
1) 6x(4+3).
Answer
4 ENTER 3 + 6 x
2) 2+{2x[2+(2/2)]}
Answer
2 ENTER 2 / 2 + 2 x 2 +

IMPORTANT: For sake of simplicity sometimes we will use / instea of ÷.
2.5 Menus
Not all functions of HP-42S are visible above the keys. It has menus with much more functions. The
menus are
ALPHA, MODES, DISP, CLEAR, SOLVER, ∫f( ), MATRIX, STAT, BASE, CONVERT,
FLAGS, PROB, CUSTOM, PGM. FCN, PRINT, TOP.FCN an 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 o this the DISP menu appears in the first line with the following functions.
FIX, SCI, ENG, ALL, RDX., RDX,
These functions appears just above ∑+, 1/x,√x, LOG, LN an XEQ. Now with DISP menu active
those keys on't represent their original functions but those of 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 using
FIX function the isplay becomes with a fixe number of igits after ecimal point.
Ok, press FIX. (I mean ∑+ with DISP menu active)
When you o this what appears is
FIX _ _
Then you have to enter a number up to 11. Example
FIX 0 4 set calculator to have 4 igits of precision after the ecimal point. A number like π will
appear as
3.1416
an √2 will appear as 1.4142.
(You can verify this by oing ▀ π an 2 √x respectively)
If you put FIX 0 9 than those numbers will appear as
3.141592654
an
1.414213562.
It is important to say that this is not the actual precision the calculator will have but just the isplay
precision. To see all calculator precision you have to press ALL in DISP menu (above LOG key).
By oing so those numbers will appear as
3.14159265359
an

1.41421356237
As you can see the numbers are not truncate but roun e .
Not all numbers can be seem with a fixe ecimal precision. If you put 4 igits for fixe precision
the number π will appear as 3.1416 but if one calculate
108
( o this by oing 8 ▀
10x
) what
you are going to see is 100,000,000.000 with 3 ecimal igits. This happens because the calculator
cannot show more than 12 igits at a same line.
2.6.2 The ALL function
We alrea y talke about 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” mo e. The numbers
will be shown as a ecimal number between 0 an 1 times a power of 10.
For example 1000 will be represente as 1.00E3 with you put the calculator in scientific mo e with
2 igits. 1.00E3 means 1.00x
103
. The π number will appear as 3.14E0.
Actually even when in FIX mo e the calculator will turn in scientific notation to give some answers.
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” an show the result in the best way as possible.
Exercise. Show that 1.0001-1 gives 1.000E-4 in FIX 3 mo e.
Answer:
First we put the calculator in FIX 3 mo e by oing ▀ DISP FIX 0 3.
Then we o 1 . 0 0 0 1 ENTER 1 – an we get the answer.
As you can see when you are in FIX mo e a sign ■ appears on the right si e of FIX name in the
DISP menu. This means FIX mo e is active. The same happens with SCI, ALL, etc.
It is out of our scope to give a full escription of scientific notation. In case of nee please report to
a first book of physics for high school or college.
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 oes not nee to be between 0 an 1 but can be between 0 an 1000 an the
power will be always 3 manifol .
Example: 100 will be represente by 100.E0 in ENG 2 mo e while 1000 will be 1.00E3 in the same
mo e. Why o we get 100.E0 for 100 instea of 100.00E2 in ENG 2 mo e? Because the calculator
shows in engineering mo e the same number of igits it shows in scientific mo e.
2.6.5 RDX. An RDX, functions
In some countries like Brazil we use ',' for ecimal point instea of '.' an also '.' instea of ',' for
1,000 an 1,000,000 etc.
For example π is written here (Brazil) as 3,141 etc an not as 3.141 etc. In FIX 3 mo e one million
is written here as 1.000.000,000 an not as 1,000,000.000 as in English use. By pressing RDX, you

make the calculator to use ',' for ecimal point an by pressing RDX. we make it use '.' for ecimal
point. Again the active mo e is followe by a ■ sing. Here, in this manual, I suppose the calculator
using '.' for ecimal point.
2.6 MODES Menu
To access MODES menu just press ▀ MODES. (MODES is above +/- key).
DEG actives egree mo e for trigonometric functions. In this mo e a circumference has 360
egrees. RAD actives ra ian mo e an in this mo e a circumference has 2π ra ians or just 2π.
GRAD is not so useful an correspon to 400 egrains for a circumference.
For example: In egrees we have sin(90°)=1 an in ra ians we have sin(π/2)=1.
Try this: ▀ π 2 / COS in ra ians mo e. Why the result is not exactly zero?
Answer: Because the number that calculator entere was not exactly π but 3.14159265359.
REC actives rectangular mo e (x,y) an POLAR actives polar mo e (r,θ). We will see this more in
etail when stu y complex numbers.
The MODES menu has another line but we will iscuss this later. We will iscuss the others menus
later too.
2.7 The Stack
No calculator can store an infinite amount of ata. In algebraic calculators the “( )” are limite to a
given number epen ing on the mo el. The same happens in RPN calculators. In some mo els like
HP-48 or HP-49 the amount of input ata is limite only by available memory. But in other mo els
like 32SII, 33S (in RPN mo e) an 42S the input ata have to fit in a “stack” of four lines.
There are four lines labele x, y, z an t. (actually the name of the last two is not so important).
So the stack is something like
t:0.0000
z:0.0000
y:0.0000
x:0.0000
But as the calculators isplay has only two lines just x an y lines are visible.
When you enter a number (say 2 ENTER) what happens is the following.
i) The content of lines t an 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 entere goes to line y an line x.
So what you just entere appears twice. So if you o 2 ENTER + you will have 4 as answer.
This is a feature, a ba feature I think, of the HP RPN style of 42S (also in 33S, 12C, etc but not in
HP48 or 49). In my opinion we coul have a simpler RPN style. Anyway there is another way to
enter ata in RPN. It is just type what you want an press the esire function key.
For example, if you o 2 1/x before the 1/x function the calculator makes an automatic enter but in

this case the content just entere appears only once.
So if you o 2 1/x or another example 9 √x what you will have will be
i) Only the content of the line 4 (line t) will be lost.
ii) The content of line 3 (z) goes to line 4 (t).
iii)The content of line y goes to line 3 (z).
iv)The content of line x goes to line y.
v) Your result will be in the first line x.
This secon way to enter ata looks more intuitive to me an I think it shoul be aways like this.
But it is not!:( So to o 2+3 we have to o
2 ENTER 3 + (an not 2 ENTER 3 ENTER +).
(Actually one can also use EXIT to enter a number without uplication)
If you just press ENTER you uplicate what is in line x.
When making a calculation one shoul 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.
The basic operations with the stack are: x><y an R↓. The first changes line x with line y. The
secon makes the stack rolls own (line y goes to line x, line x goes to line t, line t goes to line z
an line z goes to line y)
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 use to correct a number when typing it.
Another useful function is ▀ LAST which gives the last calculate result.
2.8 Getting used to some keys of the keyboard
Let's iscuss some basic keys of the calculator. We will start from superior left si e.
Σ+ an ▀ Σ- : These are statistical functions. We will iscuss this later.
1/ an ▀
yx
: 1/x just calculate the inverse of a number which is in line x.
▀
yx
is the potential function. To calculate
53
= 5.5.5 we o
5 ENTER 3 ▀
yx
.
√ an ▀
x2
: These functions just calculate the square root an the square of a number in line x.
When stu ying complex numbers we will see that unlike HP-33S in HP-42S the
number in square root can be negative.
LOG an ▀
10x
: These functions calculate the base 10 logarithms an it's inverse.
These things were important before the era of calculators so there is no reason
to have them in one.

LN an ▀
ex
: These functions calculate the base e=2.71828... logarithm an it's inverse.
Unlike LOG these are very, very important functions!
But what about if we want a logarithm in another base? It woul be nice to have a special key for
this but it is just about remembering that
logxy=logzy/logzx
where z is any other base.
If we take z=e=2.71828... we have
logxy=ln y/ln x
.
Example: Calculate
log28
Answer: 8 LN 2 LN / which give us 3 because
23=8
.
XEQ an ▀ GTO: These are relate to programming an we shall iscuss this later. XEQ will also
be iscusse in ALPHA menu part.
STO an ▀ COMPLEX : These are relate to the memories an complex numbers. We will
iscuss this later.
RCL an ▀ % : RCL is relate to memories an we will iscuss later. ▀ % is the percentage
function. To calculate 10% of 300 we o
300 ENTER 10 ▀ % which gives 30 as answer.
Note that 300 remains in line y, so if you want to calculate 300 plus 10% you o
300 ENTER 10 ▀ % +
R↓ an ▀ π : We alrea y iscuss these. The first rows own the stack an the other returns
π=3.14...
SIN an ▀ ASIN : These are the sinus trigonometric function an its inverse. The angle type is set
up as sai before in MODES menu. The efault is egrees. ASIN is the inverse
usually calle arcsine or sometimes
sin−1
. ( on't confuse with cosec 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 an ▀ ACOS: These are the cosinus trigonometric function an its inverse.
TAN an ▀ ATAN: These are the tangent trigonometric function an its inverse. Not all numbers
can have a result for tangent. For example tan(90°) goes to infinite. The
HP-42S gives a big number instea .
ENTER an ▀ ALPHA: The ENTER key oes not nee any comment. ▀ ALPHA is the alpha-
numeric menu use to enter letters instea of numbers. When you press ▀
ALPHA what appears is