A new high dynamic range moduli set with efficient reverse converter

Abstract

The Residue Number System (RNS) is a representation system which provides fast and parallel arithmetic. It has a wide application in digital signal processing and provides enhanced fault tolerance capabilities. In this work, we consider the 3-moduli set { 2 n , 2 2 n − 1 , 2 2 n + 1 } and propose its residue to binary converter using the Chinese Remainder Theorem. We present its simple hardware implementation that is mainly composed of one Carry Save Adder (CSA), a 4 n bit modulo 2 4 n − 1 adder, and a few gates. We compare the performance and area utilization of our reverse converter to the reverse converters of the moduli sets { 2 n − 1 , 2 n , 2 n + 1 , 2 2 n + 1 } and { 2 n − 1 , 2 n , 2 n + 1 , 2 n − 2 ( n + 1 ) / 2 + 1 , 2 n + 2 ( n + 1 ) / 2 + 1 } that have the same dynamic range and we demonstrate that our reverse converter is better in terms of performance and area utilization.