Two's complement – You beauty

> I was not curious to ask what is the need for one's complement or two's complement.

A problem with school, not the student (a common problem IMHO).

Good write up!

And groups!

By the time you have implemented enough silicon for floating point addition and multiplication, the amount of extra transistors you would need to special case the compare operator's zero case is realtivily tiny.

The same can not be said for an interger alu (especially one without hardware multipliers or even arbitrary bit shifts), where twos complement representation can save a much larger percentage of silicon.

Shitty C code: the binary printing function is needlessly complicated.

    void print_bin(int x){  
	for(unsigned m=~(~0u>>1); m ; m>>=1)  
		putchar(x&m?'1':'0');  
	putchar('\n');  
    }

> What _is_ annoying about the UNISYS boxes is the 36 bit word format, though. Characters are stored in 9 bit quarterwords that map pretty awkwardly to bytes containing 8-bit ASCII. Binary data formats are essentially incompatible with anything.

This is why the FTP protocol has a byte size command. If all you have is 8-bit bytes then that seems strange. But at the time FTP was designed the most common machines on the ARPANET had 36-bit words (mostly PDP-10s and their derivatives) and bytes (the term was used in the more general sense) were just bit strings of 1-36 bits. 7-bit ascii was common (5 characters would fit in a word, like my username GUMBY), as were six bit bytes (pack six characters into a word). I never used 9-bit characters though arrays of nine-bit bytes were not unreasonable.

BTW the PDP-10 had 18-bit addresses so each word of memory held a Lisp cons; CAR, CDR, RPLACA etc were machine instructions. Gordon Bell and Alan Kotok designed the -10 (and its predecessor the PDP-6) with Lisp in mind. The first Lisp Machines.

> Binary data formats are essentially incompatible with anything.

Well, that's true today, but look at it the other way around: Unix was really developed for an 8/16-bit machine. It was a reimplementation of Multics that ran on a 36-bit machine (GE 645 & Honeywell 6180) written in PL/1. Unix was famously written for the PDP-7 (an 18-bit machine) but it was written in assembly. The famous PDP-11 version was written in a BCPL derivative you might have heard of called "C" and, since PL/1's level of machine abstraction was still new, the derivative modeled the PDP-11 architecture. So nowadays all CPUs are C machines and C runs well on them. Probably the most common non-PDP-11-like machine most programmers will program these days is a GPU.