New algorithm for signed integer comparison in four-moduli superset {2n, 2n −1, 2n +1, 2n+1−1}

Abstract

Sign detection and magnitude comparison are two difficult operations in Residue Number System (RNS). Existing residue comparators tackle only unsigned integer for magnitude comparison. In this paper, a new algorithm for signed integer comparison in the four-moduli supersets, {2n, 2n -1, 2n +1, 2n+1-1} with even n, is proposed. The dynamic range is quantized into equal subranges to facilitate fast sign detection and magnitude comparison simultaneously without the need for full magnitude recovery by Chinese Remainder Theorem (CRT) or sequential Mixed Radix Conversion (MRC). The proposed algorithm can be implemented by using adders only and the operations are less complex than those used in existing RNS magnitude comparators of comparable dynamic range.