Newsgroups: comp.arch
From: hoey@zogwarg.etl.army.mil (Dan Hoey)
Date: 27 Nov 92 18:29:18 GMT
Subject: Re: Summary: Integers implementation

fa...@gr.osf.org (Christian Fabre) writes:

>For integers arithmetics, 2's complement is the most
>used nowdays with a BIG advantage over 1's complement and
>sign-magnitude: only one representation of 0. Another
>advantage is that size extension is more [convenient].

Actually, it's more that sign extension makes sense.  Which is to say
that converting an n-bit twos-complement number to an m-bit number,
the low-order min(m,n) bits don't change.  So the sign bit does not
usually require a lot of extra logic.

>1's complement was used (e.g. PDP11, CDC), buts its advantage
>of fast negation and symetrical ranges around zero does not
>balance the 2 zero problem.

The PDP-11 used twos complement.  But another use of ones complement
is in checksum calculations.  I think the advantage is that if you
want to find the ones-complement sum of a bunch of n-bit bytes, you
can add them up k at a time as a bunch of kn-bit bytes, and then add
together the k n-bit bytes in the sum.  This saves time when your
machine has wide instructions.

>sign-magnitude and excess-n are used to represent floating
>points number (mantissa and exp, respectively).

I'm pretty sure twos complement is often used for the mantissa, too.
Excess-n, where n = 2^(# bits - 1), is just twos complement with the
top bit complemented.  I recall that with a twos complement mantissa
and an excess-n exponent, you can use twos complement integer
comparisons on floating point numbers.  As far as I know, that's the
only reason to favor excess-n over twos complement for the exponent.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil