HP35 Operating software

1) Overall firmware architecture Designed during the period 1970-1972, the HP 35 was using a specialized processor consisting in 2 MOS chips the “Control and Timing” circuit (C&T) and the “Arithmetic and Registers” circuit (A&R). The firmware was stored in 3 ROM, each of which contained 2560 bits of information (a total of 7680 bits). Around 30000 MOS transistors were crammed in the 5 MOS LSI circuits and almost the third of the firmware (2540 bits) was used by service routines operating the calculator. In the present article, I will study this “operating software”, that is to say, the code used to make the machine working, from power on to the display of a result.

The architecture of the calculator is quite canonical and is a common denominator of this class of machine at that time (HP, TI, Sharp and others).

I summarize it in the diagram left.

Compared to the late 70’s Basic Rom systems (like MITS Altair or TRS80), the calculator software is much simpler:

-  there is only one state: the “run” mode,
-  the Rom is much smaller (8 Kbits vs 4Kbytes for the first version of the MITS ALTAIR – 1975),
 -  input are only floating point numbers.

The working model can be summarized in a few words:

Step 1: the system runs a prologue code where registers are initialized,
Step 2: with a display context properly formatted, the system enters in its wait state, looping to display the former result (can be “0.”) and waiting for a user interaction,
Step 3, the user has hit a key, the key code returned by hardware is a displacement to calculate the ROM address of the routine to execute,
Step 4: when routine’s execution is over, output is again formatted and the system re-enter in the wait loop.

Let’s dig a bit.

1) At power on time (PWO) when the slide is “on” and when the power is applied, the system jumps to ROM address 0000, This is the initialization sequence but the same code will be executed later for CLR key service.

The sequence clears registers, clears status bits and set up the pointer. Another entry point in this code exist for the CLx keys, the cleaning is not so hard and the C register is preserved (display).

2) Secondly, the system enters in a routine that soon will become familiar: Output Format (of13). There the proper context for display will be built:

- in register C the number in normalized form,
- in register A, the number in floating point form,
- and in B the display mask.

I will detail below this 3 form representation.

If the calculator is in the PWO or CLR mode, the first number is zero and the display built is “0.”

3) Third, the machine is entering in its “idle” state doing what it does when it does nothing: display and wait_a_key loop (dsp). There the life is easy, displaying the previous result (X in C register) and waiting for a key to be hit.

Logically, the user would now enter data. Digits entered are processed in the “den” and “eex” group of routines. “Den” (“digit entry”) is making a floating point number and a mask out of individuals digits, “.” and possibly “EEX”, while “eex” is building normalized mantissa and exponent.

When the number is entered, back to the farm in the “dsp” display and wait loop.

If instead of digit, a service key is pressed, the “action” code is immediately executed.
Keys are decoded by the system as a key code number made from the keyboard matrix. When the user presses the “1” key, the key code buffer holds the value “34”: address 034 (octal) is the entry point for “digit 1” routine. 

Note that “key code” is very similar to “token” in a Basic ROM system (the action verbs were entered in ASCII but stored as a token internally): it is a displacement on the entry points table.

Now, the machine is ready to perform a calculation: if the user press the “ln” key (key code 06), the operating system will branch to address 006, which is the entry point of the log routine.

The routine code performs the calculation, at the end a normalization of the result is applied (nrm21), the OS branches to “of” routine to format the output (build floating point and mask representation) and next to “dsp”, to display result and wait the next key.

If the user wants to do a dyadic (2 number) function, the ENTER key must be used to push the first number on the stack, the second number is  entered and the operation (say +) must be applied.

This article will cover all the operating software (open chapters with left buttons):

-         data entry digit by digit and building numbers in A, B and C registers (mainly routines “den” and “eex”),
-    normalization of a result on exit from a math routine,
-         output formatting which makes A and B registers from a normalized result,
-         display and wait loop (April 2006),
-         the 4 level RPN stack (April 2006),
-         the status bit flags (April 2006),
-         the key codes tokens,
-         the rest of the service routines (keys ENTER, CHS, CLR, CLx, STO, RCL etc,) that are not treated in the mathematical articles (April 2006).

This will complete the full software reverse engineering of the HP 35 firmware.