Path: utzoo!attcan!uunet!convex!killer!ames!umd5!uvaarpa!virginia!uvacs!wulf From: wulf@uvacs.CS.VIRGINIA.EDU (Bill Wulf) Newsgroups: comp.arch Subject: more on unsigned Message-ID: <2433@uvacs.CS.VIRGINIA.EDU> Date: 30 May 88 16:18:35 GMT Organization: U.Va. CS Department, Charlottesville, VA Lines: 53 I must admit to being a bit overwhelmed by the number and diversity of articles that have appeared in response to my querry about machines with negative addresses. First, thanks to all. Second, apologies for not responding to them; I just started a new job at NSF and have been pretty busy -- just reading them on weekends has been the best I could do. Third, I want to correct one rampent mis-impression. Unsigned is NOT required for multi-precision arithmetic. This is hardly the forum for a lecture on arithmetic, but, just to set the framework -- as we all know, our familiar positional notation is simply a shorthand for a polynomial. Eg, 123 == 1*10**2 + 2*10**1 + 3+10**0 the numeral in "123" are simply the coefficients of the polynomial, and their position is used as an abbreviation for the "10**n". Now, a multi-precision number can be thought of in the same way. That is, each word can be viewed as a coefficient in a polynomial of the form w2 w1 w0 == w2*(2**32)**2 + w1*(2**32)**1 + w0*(2**32)**0 NOW -- no one ever said that these coefficients must be positive!!! Perfectly reasonable, consistent number systems can be defined where some of the numerals denote negative values. Consider a ternary number system where the numerals are 1 == 1 0 == 0 M == -1 SO, for example, 1M0 == 1*9 + (-1)*3 + 0*1 == 6, and decimal is strange ------- ------- 0 0 1 1 2 1M 3 10 4 11 5 1MM 6 1M0 7 1M1 8 10M 9 100 etc. So, you see, while it may seem a bit strange, unsigned arithmetic is not necessary for multi-precision arithmetic. Bill