Sign Identifier for the Enhanced Three Moduli Set {2n + k, 2n − 1, 2n+ 1 − 1}

Abstract

The three-moduli set {2n,2n − 1,2n+ 1 − 1} started to receive more attention lately. This moduli set is considered an arithmetic-friendly set because it avoids the demanding channel (2n + 1) of the traditional 3-moduli set {2n,2n − 1,2n + 1}. This work considers an enhanced form of the above moduli set, {2n + k,2n − 1,2n+ 1 − 1}, and proposes a sign identifier for numbers within the dynamic range of the set. While the published sign identifiers have dealt with the unextended form {2n,2n − 1,2n+ 1 − 1}, this is the first sign identifier that deals with the extended form. Based on VLSI layout synthesis for the case (k = 0), the proposed structure has less or similar area and power requirements, nevertheless, it achieves an improved time performance in the range of (13.0–29.6)% compared with the most recent sign identifiers. When compared with a recently published residue-to-binary converter for the moduli set {2n + k,2n − 1,2n− 1 − 1}, which can function as a converter-based sign identifier, the proposed detector has on average reduced area, time, and power by 175%, 106%, and 60%, respectively.