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Weighted two-valued digit-set encodings: Unifying efficient hardware representation schemes for redundant number systems
, Article IEEE Transactions on Circuits and Systems I: Regular Papers ; Volume 52, Issue 7 , 2005 , Pages 1348-1357 ; 10577122 (ISSN) ; Parhami, B ; Ghodsi, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2005
Abstract
We introduce the notion of two-valued digit (twit) as a binary variable that can assume one of two different integer values. Posibits, or simply bits, in {0, 1} and negabits in {-1, 0}, commonly used in two's-complement representations and (n, p) encoding of binary signed digits, are special cases of twits. A weighted bit-set (WBS) encoding, which generalizes the two's-complement encoding by allowing one or more posibits and/or negabits in each radix-2 position, has been shown to unify many efficient implementations of redundant number systems. A collection of equally weighted twits, including ones with non-contiguous values (e.g., {-1, 1} or {0, 2}), can lead to wider representation range...