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From: faiman@uiuccsb.UUCP
Newsgroups: net.arch
Subject: Re: Re: Complement Arithmetic - (nf)
Message-ID: <5243@uiucdcs.UUCP>
Date: Mon, 30-Jan-84 22:32:08 EST
Article-I.D.: uiucdcs.5243
Posted: Mon Jan 30 22:32:08 1984
Date-Received: Tue, 7-Feb-84 06:35:22 EST
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#R:burdvax:-142500:uiuccsb:5600004:000:1446
uiuccsb!faiman    Jan 30 08:33:00 1984

I was both amused at, and sympathetic towards Bill Hopkins' remarks about
one's complement arithmetic and his difficulty in coming up with a good
argument for using it other than symmetry of range, which property,
incidentally, is also possessed by signed magnitude.  I have taught ye
goode olde standarde digitale designe course off and on for quite a few
years and have got used to the fact that most textbook authors on the
subject are content to list the common forms of number representation
without giving any reasons why a designer might want to choose one over
another in a given application.  The pricipal virtues of two's complement,
biassed, and signed-magnitude are, of course, well known, but for many
years I could find nothing good to say about one's complement, being
unimpressed by the "ease of implementation" argument that used to be
fashionable around, maybe, 1950.  However, consider the problem of a
poor soul who wants to build a (fixed point, of course) signed-magnitude
adder.  A simple way of thinking about this, and not a bad way to
implement it either is first, to convert from SM to 1C, a trivial and
fast operation; next, add with end-around carry; and, finally, convert
back to SM, an operation identical to the first.  That's a pretty far-
fetched reason, I hear you say.  Well, perhaps someone from the frozen
wastes of Minneapolis can produce some better ones.

(From the frozen wastes of Urbana) - Mike Faiman