With my mind on our upcoming AHRC weave/code project (and seeing as Alex has already started writing code) I thought I’d have a go at visualising how computers work in relation to pattern manipulation. These screenshots are from a ZX Spectrum where I’ve modified some library assembler code for higher level arithmetic to display the contents of 7 CPU z80 registers graphically between each instruction – time runs from top to bottom.
Most processors don’t actually have circuits for mathematics, they simply implement ‘add’ along with bitwise instructions for ‘and’, ‘or’, ‘not’, ‘xor’ and a handful of instructions for shifting the bits left and right. This is true even with modern CPU’s where the arithmetic instructions for multiply, divide etc are built with hidden ‘microcode’ routines. For this reason the underlying operation of a computer has more to do with patterns than it does with concepts such as language or even numbers as we normally think of them.
The simplest (and shortest) are multiply in 8 bits. In this function, the ‘a’ register contains one number and the ‘h’ register contains the other – at the end the ‘a’ register contains the result. In the first screenshot the numbers are fairly simple so it’s possible to see what’s going on (ie. in 1*1 the ‘a’ and ‘h’ registers both contain 00000001)
170 in 8 bits looks like ‘10101010’ so easy to see – here are some different ways of reaching the same answer:
16bit multiply operates over 2 registers – the first value is stored in ‘h’ and ‘l’ and the other is on the stack, but is loaded into ‘d’ and ‘e’ after a few instructions:
43690 is ‘1010101010101010’ so in the first run here we multiply it by one as a test:
Some 16 bit divides – these take a longer time to calculate, so a whole page for all the instructions involved, and I have no idea how this works:
65535 is the largest value we can store, divide by itself to end up with 1:
The code for all this is here.
