An efficient residue-to-binary converter for the moduli set {2n−1−1, 2n+k, 2n−1}

Abstract

In this paper, a RNS (Residue Number System) to Binary converter for the three-moduli set {2ⁿ⁻¹−1, 2^n+k, 2ⁿ−1} using two-stage Mixed Radix Conversion (MRC) is presented. Two separate cases (a) 0 ≤ k ≤ n-2, and (b) k = n−1, k = n lead to two different reverse converters. The proposed reverse converters are evaluated and compared with state of the art reverse converters proposed for this moduli set regarding hardware requirement and conversion time.