MRC Technique for RNS to Decimal Conversion Using the Moduli Set

This paper investigates the conversion of Residue Number System (RNS) operands to decimal, which is an important issue concerning the utilization of RNS numbers in digital signal processing applications. We present a Mixed Radix Conversion (MRC) technique for efficient RNS to decimal conversion using the moduli set {2n + 2, 2n + 1, 2n}, which has a common factor of 2. First, we provide two important theorems which show that, using such a moduli set, the computation of multiplicative inverses can be eliminated. The usage of these theorems with the traditional MRC results into two reverse converters. In terms of area, the proposed converters require 3 adders, 4 mutipliers and mod-m2 and m3 operations. The proposed converters also require 2 additions, 2 multiplications with mod-m3 operation in terms of critical path delay. Our proposals outperform state of the art equivalent Chinese Remainder Theorem (CRT) based reverse converter in terms of delay and due to the fact that the numbers involved in the calculations are smaller it results in less complex adders and multipliers.