An Alternative hp-42S/Free42 Manual

2.7 MODES Menu

To access MODES menu just press  MODES. (MODES is above +/– key).

DEG activates 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. t stands for top, it is the STACKTOP. Notice that there are some software modifications to free-42 on the “Apple i-phone touch” allowing for an “infinite” (limited by RAM amount only) stack depth. This is a nice feature but the user must be aware of stack depth during RPN calculations to care for dropped and replicated values on the stack, affecting the result of the calculation. The result of a RPN program can alter with altering the stack depth (possible loss of software compatibility). Throughout this manual we assume stack depth to be 4 (using X, Y, Z, T) which is a standard in HP calculators.
X is the “display register”, the one you see most of the time.
The ENTER key runs a STACKLIFT. Mathematical functions result in a STACKDROP, where T is replicated into Z (also if T was zero).
Today, no calculator can store an infinite amount of data. In algebraic calculators the “( )” are limited to a given depth 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. Assume the stack is
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.

1. 
   The content of lines t and z are lost.
   
2. 
   The content of line y goes to line t.
   
3. 
   The content of line x goes to line z.
   
4. 
   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

1. 
   Only the content of the t register will be lost.
   
2. 
   The content of the z register goes into the t register.
   
3. 
   The content of y goes into z.
   
4. 
   The content of x goes into y.
   
5. 
   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 +). 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 real numbers but also matrices, complex numbers, etc.. Note that the handling of complex numbers on the stack varies slightly throughout different models of HP calculators.

Two basic operations with the stack are: x<>y and R↓ (ROLL DOWN). 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). R↑ does a ROLL UP via RPN program.
In the CLEAR Menu there are some interesting functions: CLST (clear stack) which clears all the stack (something missing in HP-33S). CLX clears the line x in the same way of pressing ← . The ← is rather used to correct a number when typing it. Another useful function is  LASTx which gives the last calculated result. It is useful if when you work with constants.

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  y^x The 1/x key just calculates the inverse of a number which is in register x.  y^x 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 log_z 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 ▼ we use this to change the line in a multi line menu.
We will see  BST BACKSTEP and  SST SINGLE STEPING later.
The digit keys from 0 to 9 have their obvious function for entry of numbers into the X Register of the stack.
. and  SHOW: The '.' is just the decimal point and  SHOW is used to show a number for an instant with full 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.