Understanding output width in signed multipliers

Yes.

In a two's-complement multiplication with inputs S+n and S+m, where S represents a sign bit and n, m represent the number of remaining bits, the product will have dimensions 2S+n+m in all cases except

10...0*10...0 (i.e., max neg times max neg). If you can avoid this case, you can throw away the redundant-sign-bit MSB.

How to avoid it? You can, as suggested, use a clipper to limit one of the inputs to a negative value of 10...01. Or if, as is often the case, one of the inputs comes from a coefficient table, you can select/scale your coefficients to avoid the max. negative number.

Obligatory clarification for those who care: In casual conversation (i.e., at parties, coronations, parole hearings) we often refer to the MSB of a two's-comp number as the sign bit. It's more accurate to call it a magnitude bit with a negative weight. For example, the bits in a 4-bit, two's-comp number have weights (from MSB to LSB) of -8, 4,

2, and 1. Looking at two's-comp this way removes a lot of the mystery from two's-comp arithmetic.

Bob Perlman Cambrian Design Works

Bob Perlman wrote: : Obligatory clarification for those who care: In casual conversation : (i.e., at parties, coronations, parole hearings) we often refer to the : MSB of a two's-comp number as the sign bit. It's more accurate to : call it a magnitude bit with a negative weight. For example, the bits : in a 4-bit, two's-comp number have weights (from MSB to LSB) of -8, 4, : 2, and 1. Looking at two's-comp this way removes a lot of the mystery : from two's-comp arithmetic.

Nice explanation! Thanks

--
Uwe Bonnes                bon@elektron.ikp.physik.tu-darmstadt.de

Institut fuer Kernphysik  Schlossgartenstrasse 9  64289 Darmstadt
--------- Tel. 06151 162516 -------- Fax. 06151 164321 ----------

Absolutely, Bob. Once my parole officer explained this to me, designing distributed arithmetic multipliers became a walk in the park! Cheers, Syms.