An Efficient RNS to Binary Converter Using the Moduli Set

In this paper, we investigate Residue Number System (RNS) to decimal conversion which is an important issue concerning the utilization of RNS numbers in Digital Signal Processing (DSP) applications. We propose a reverse converter using the moduli set {2n+1, 2n, 2n−1}. First, we show that this converter does not require the computation of multiplicative inverses. Next, we simplify the Chinese Remainder Theorem (CRT) to obtain a low complexity implementation, which does not require explicit use of modulo operation in the conversion process as it is normally the case in the traditional CRT. At the algorithm level the conversion process requires 3 or 4 additions and 4 multiplications thus theoretically speaking its expected performance is similar to that of other state of the art equivalent converters. A critical path analysis however, which takes into consideration hardware implementation details, indicates that the proposed converter outperforms other state of the art converters in terms of speed at the expense of same or lower area.