This is a replacement firmware for the [diyleyuan calculator](http://www.diyleyuan.com/jc/L8Q.html) using the STC IAP15W413AS microcontroller, which uses the 8051 instruction set. It uses SDCC to compile the C code and [stcgal](https://github.com/grigorig/stcgal) to load the new firmware.
The STC microcontroller used has a bootloader permanently stored in ROM that allows downloading new firmware over a serial port. You can re-program it using a USB to logic level (5V) serial dongle, and the stcgal program. WARNING: a lot of USB to logic level serial dongles are for 3.3V logic levels. The diyleyuan calculator runs at 5V to make it easier to power/drive the LCD display. You have a couple of options:
1. get a USB to logic level serial dongle that supports 5V operation (there may be a jumper you have to set to switch between 3.3V and 5V). This is the best option.
- here is one that works: https://www.amazon.com/gp/product/B00N4MCS1A/
1. if you have an adjustable power supply, power the diyleyuan calculator at 3.3-3.5V for programming, instead of 5V, and use a 3.3V USB to logic level serial dongle.
You must "cross over" TX/RX going between the microcontroller and the USB dongle (i.e. RX on the microcontroller goes to TX on the USB dongle, and TX on the microcontroller goes to RX on the USB dongle).
Be careful when working on the calculator. The 7550 voltage regulator used has no short circuit protection. It does have a very low quiescent current and low dropout voltage though. If you do end up damaging the regulator (like I did), a good replacement is the Microchip MCP1700-5002E/TO. In the picture, I have removed the 7550, shorted pins 2 and 3, and added a capacitor between pin 1 and pins 2/3. I am powering the calculator externally.
Here is the schematic from the diyleyuan website. Note that the schematic symbol for the microcontroller mistakenly labels P5.4 as P0.0, and mistakenly labels P5.5 as P0.1. The net name labels are correct.
The soft-latching power switch works as follows. Initially the calculator is off. Both Q1 and Q2 are off. Pressing the On key (S4) turns on Q1 through R1 and D2. Then, once the microcontroller has power, it turns on Q2, which keeps Q1 on through R1. To turn off, the microcontroller turns off Q2, which in turn will turn off Q1.
Here is the component layout from the diyleyuan website.
The switches used are a knockoff of the Omron B3F series. A good replacement is the B3F-5050. The LCD used is a fairly standard LCD based on a HD44780-compatible controller. The hole spacing for the screw holes on the LCD is 31mm x 75mm. There are many replacements available, including ones that don't need the backlight on to be readable. I recommend a postive FSTN type, although the one included is definitely usable.
See below for the stcgal output. Replace stc_rpncalc/main.hex with the actual path to the main.hex you built. This example is done at a high line rate of 230,400 bits/s. You may want to try at a slower speed 1st to get things working (omit the `-b 230400` option).
1. Currently, trying to display numbers between `[0.1, 1)` causes the calculator to crash.
1. There are probably more bugs waiting to be discovered.
# Internals
## Number Format
The original firmware that came with this calculator used a fixed point format, which limited the range of numbers. Also, the implementation was slightly buggy (e.g. `3,162.277*3,162.28` gives `10,000,010` instead of the correct `10,000,005.31156`).
This calculator firmware uses decimal floating point, using base-100 to store numbers and do calculations. Base-100 allows efficient storage into 8-bit bytes, and is easier to work with than packed-BCD. Unlike binary representations, base-100 is still fairly easy to display in decimal. Also unlike binary representations, there is no conversion error from binary/decimal (e.g. numbers like `0.1` can be represented exactly).
Each `uint8_t` stores a base-100 "`digit100`", referred to as an "`lsu`" (least significant unit: the terminology is borrowed from the decNumber library). The format is as follows:
-`lsu[0]`: contains the most signifcant `digit100` (the most signifcant 2 decimal digits)
- implicit decimal point between `lsu[0]/10` and `lsu[0]%10`
-`lsu[1-n]`: the reset of the array contains the next `digit100`s in order from most to least signifcant
- exponent: holds the exponent of the floating point number
- stored directly in 2's complement binary
- this is a base-10 exponent, not a base-100 exponent
- allows all digits in the `lsu[]` array to be significant when normalized
- otherwise numbers such as `1.35` would be stored as `lsu[0]=01`, `lsu[1]=35`, losing 1 digit of representation in `lsu[0]`
- range of exponents only needs to be `+/-99`
For example, the number `13.5` is stored normalized (with no leading zeros in the representation) as follows:
-`lsu[0]`: 13
-`lsu[1]`: 50
-`lsu[2-n]`: all zero
- exponent: 1
There is an implicit decimal point between the 1 and 3 in `lsu[0]`, so the number is 1.350 * 10^1, which is equivalent to 13.5. Similarly, the number 1.35 would be stored the exact same way, except now the exponent is 0.
## Arithmetic
- Addition is done the same way as it's done by hand, although in base-100 instead of decimal.
- Subtraction is similarly done similar to how it's done by hand, although with carries instead of borrows using the "equal additions" algorithm, and also in base-100.
- Multiplication is done the same way it's done by hand, although in base-100. Partial sums are added up and shifted after each digit, instead of waiting until the very end to sum up all partial sums, as is common when doing multiplication by hand.
This was my 1st time using an 8051 microcontroller. The architecture is a bit limiting for programming in C compared to more modern architectures -- even compared to other 8-bit microcontrollers such as the AVR. Most significantly, there is no stack-pointer-relative addressing, which makes C functions takes up a lot of code space, since they must emulate stack-pointer-relative addressing. Unfortunately, the microcontroller used only has 13K of code space, which is pretty limiting. It's almost completely full just doing a 4 function decimal floating point calculator.
I've avoided relying on the functions being able to be reentrant, so that they do not depend on having a stack. Some "large" variables are declared as static in functions to save on the code space needed to emulate a stack.
Another weird thing about the 8051 is that not all of the memory is addressed the same way. On this microcontorller, there are 512 bytes of ram total, of which:
Thus, there are special compiler directives to tell it where to place things in memory. (Even for a simple calculator, there isn't enough directly addressable memory (128 bytes) to store everything.)
Currently all of the code space is full, although there are ways to free some of it up. This would involve changing the code and build to not use `--stack-auto`. After doing so, it might be possible to add back in square root (using newton's method), maybe logarithms/exponents (and thus arbitrary powers including square roots), and maybe if there's still space left, the original resistor value calculator and the decimal/hex converter.
