On combinational logic for sign detection in residue number systems

Abstract

This paper is concerned with the algebraic sign detection of a number in a residue number system. The proposed solution is applicable only to nonredundant systems. The method utilizes a systematic decomposition of the sign function S that is based on some special properties of S. Starting with the canonical sum-of-products expression for S, we transform the expression to a form whose realization is simpler than the canonical form realization and, if possible, also simpler than the minimal sum-of-products realization. In some cases, the proposed method yields savings as high as 85% compared to the minimal sum-of-products realization for S.