Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!floyd!harpo!ihnp4!inuxc!pur-ee!uiucdcs!uiuccsb!faiman 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 Lines: 25 #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