Xref: utzoo sci.math:7260 comp.misc:6532 Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ncar!ico!auto-trol!douyou From: douyou@auto-trol.UUCP (Doug Young) Newsgroups: sci.math,comp.misc Subject: Re: Base 3 computers? (was: Divide by three?) Summary: 3's complement numbers Message-ID: <204@auto-trol.UUCP> Date: 10 Jul 89 22:11:03 GMT References: <6710021@hpcupt1.HP.COM> <548@skye.ed.ac.uk> Organization: The Chaos Group Lines: 29 In article <548@skye.ed.ac.uk>, ken@aiai.ed.ac.uk (Ken Johnson) writes: > In article <626@hrc63.co.uk> pj@hrc63.co.uk (Mr P Johnson "Baddow") writes: > > > >I have been trying to figure out how it [a base-3 computer] could work. > > One way would be to operate it to base 3 but have three digits > +1, 0 and -1. It is handy to use the characters P, M, and Z to represent +1, -1, and zero, respectively. Also, note that taking the "3's complement" of a number involves simply replacing P with M, M with P, and leaving Z as Z. For example PMZ ( (+1)9 + (-1)3 + (0)1 = 6 ) yields MPZ ( (-1)9 + (+1)3 + (0)1 = -6 ). To the digital mind, this may seem awkward. But consider circuitry which has three voltage levels: below a certain negative threshold is M, above a certain positive threshold (the same as TTL, perhaps) is P, and in between is interpreted as Z. In fact, one company is actually developing base 3 ("ternary"? "trinary"?) chips. It turns out you can avoid the carry-lookahead problem that plagues binary logic by going to tri-state logic. The new problem, however, is efficient conversion between the two representations. You win a few, you lose a few. Douglas Young ico!auto-trol!douyou Auto-trol Technology 12500 N. Washington Denver, CO 80241 (303)252-2418