Earlier quoted context omitted.
And groups!
Don't forget about rings.
I always found those ideal.
Two's complement – You beauty
41–50 of 92 posts
Re: Two's complement – You beauty
#42There is that wierd number 100000...0000 which is that extra negative number with no positive analog. I'm currently working with a noninteger value representation system that hijacks this value and assigns it as +/- infinity (negation is two's complement)
Re: Two's complement – You beauty
#43I program a UNISYS 2200 mainframe at work. It uses 1's complement. Yes, there are two zeros. Not a problem in practice because all arithmetic operations normalize -0 to +0 at no extra cost in execution time, so -0 practially doesn't happen. IIRC from Assembler class, addition is implemented as subtraction of the negative operand. Just in case anyone ever needs it, e.g. for bitmaps, the SZ (store zero) assembler instr…
I programmed UNISYS 1100's in 1980. Awesome beasts.
Re: Two's complement – You beauty
#44I program a UNISYS 2200 mainframe at work. It uses 1's complement. Yes, there are two zeros. Not a problem in practice because all arithmetic operations normalize -0 to +0 at no extra cost in execution time, so -0 practially doesn't happen. IIRC from Assembler class, addition is implemented as subtraction of the negative operand. Just in case anyone ever needs it, e.g. for bitmaps, the SZ (store zero) assembler instr…
> I program a UNISYS 2200 mainframe at work.
This sounds awesome. I had no idea UNIVAC is still alive.
Re: Two's complement – You beauty
#45I program a UNISYS 2200 mainframe at work. It uses 1's complement. Yes, there are two zeros. Not a problem in practice because all arithmetic operations normalize -0 to +0 at no extra cost in execution time, so -0 practially doesn't happen. IIRC from Assembler class, addition is implemented as subtraction of the negative operand. Just in case anyone ever needs it, e.g. for bitmaps, the SZ (store zero) assembler instr…
> 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…
> 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.
The Stanford PDP-6 apparently even had a CONS instruction at opcode 257 :)
Re: Two's complement – You beauty
#46I program a UNISYS 2200 mainframe at work. It uses 1's complement. Yes, there are two zeros. Not a problem in practice because all arithmetic operations normalize -0 to +0 at no extra cost in execution time, so -0 practially doesn't happen. IIRC from Assembler class, addition is implemented as subtraction of the negative operand. Just in case anyone ever needs it, e.g. for bitmaps, the SZ (store zero) assembler instr…
> 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…
> 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)
There were a bunch of different six bit character encodings, often (though not always strictly correctly) called "BCD". The horror show of IBM's EBCDIC was an eight bit extension of one of these.
Then there was 5 bit Baudot code, and...
The last time I checked, many *nix systems will still assume that you're on a 5 bit Baudot (uppercase only) teletype (i.e., a genuine physical tty) if you attempt to log in using all uppercase in your user name.
Some systems hacked in more characters by having special "shift in" and "shift out" characters. If a "shift in" character appeared in the stream, the system would switch to the alternate character set until a "shift out" character was received.
Re: Two's complement – You beauty
#47Earlier quoted context omitted.
That's a reasonable tradeoff for Python, but it's worth noting that there is a way to deal with this. Quoting from http://reference.wolfram.com/language/tutorial/IntegerAndNum... Bitwise operations are used in various combinatorial algorithms. They are also commonly used in manipulating bitfields in low‐level computer languages. In such languages, however, integers normally have a limited number of digits, typically…
Yes, but how would you print that infinite sequence of 1s?
same as the infinite number of zeros in front of a positive number.
Re: Two's complement – You beauty
#48It's an elegant construct, but this used to be a part of an entry-level course in every computer school I know of. Have things changed now?
My thought exactly when I read this kind of articles. Am I that old that they don't teach those simple concepts anymore?
Re: Two's complement – You beauty
#49I program a UNISYS 2200 mainframe at work. It uses 1's complement. Yes, there are two zeros. Not a problem in practice because all arithmetic operations normalize -0 to +0 at no extra cost in execution time, so -0 practially doesn't happen. IIRC from Assembler class, addition is implemented as subtraction of the negative operand. Just in case anyone ever needs it, e.g. for bitmaps, the SZ (store zero) assembler instr…
> 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…
There are also other interesting uses for odd word lengths. For example, many UARTs support word lengths from 5 to 9-ish bits (some do more). This is commonly used to implement out of band signalling for protocols running over these, eg. using 9 bit words, where the ninth bit tells whether this is the start of a command frame. More handily even, in most MCUs this is already correctly separated, ie. there is a byte register with the lower 8 bits and then there is a different register for the remaining bits.
Re: Two's complement – You beauty
#50Earlier quoted context omitted.
Yes, but how would you print that infinite sequence of 1s?
same as the infinite number of zeros in front of a positive number.
Just trimming 1s would be ambiguous. Is b11 3 or -2?
You would have to add a 0 prefix to all positive numbers or some other to negative.