Efficient Reverse Converter Designs for the New 4-Moduli Sets \ -1, 2^, 2^ +1, 2^-1\} and \ -1, 2^ +1, 2^, 2^ +1\} Based on New CRTs

In this paper, we introduce two new 4-moduli sets {2 n -1, 2 n , 2 n +1, 2 2n+1 -1} and {2 n -1, 2 n +1, 2 2n , 2 2n +1} for developing efficient large dynamic range (DR) residue number systems (RNS). These moduli sets consist of simple and well-formed moduli which can result in efficient implementation of the reverse converter as well as internal RNS arithmetic circuits. The moduli set {2 n -1, 2 n , 2 n +1, 2 2n+1 -1} has 5 n -bit DR and it can result in a fast RNS arithmetic unit, while the 6 n -bit DR moduli set {2 n -1, 2 n +1, 2 2n , 2 2n +1} is a conversion friendly moduli set which can lead to a high-speed and low-cost reverse converter design. Next, efficient reverse converters for the proposed moduli sets based on new Chinese remainder theorems (New CRTs) are presented. The converter for the moduli set {2 n -1, 2 n , 2 n +1, 2 2n+1 -1} is derived by New CRT-II with better performance compared to the reverse converter for the latest introduced 5 n -bit DR moduli set {2 n -1, 2 n , 2 n +1, 2 n-1 -1, 2 n+1 -1}. Also, New CRT-I is used to achieve a high-performance reverse converter for the moduli set {2 n -1, 2 n +1, 2 2n , 2 2n +1}. This converter has less conversion delay and lower hardware requirements than the reverse converter for a recently suggested 6 n -bit DR moduli set {2 n -1, 2 n +1, 2 2n -2, 2 2n+1 -3} .