Efficient Reverse Converter Designs for the New 4-Moduli Sets {2n-1, 2n, 2n+1, 22n+1-1} and {2n-1, 2n+1, 22n, 22n+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 5n-bit DR and it can result in a fast RNS arithmetic unit, while the 6n-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 5n-bit DR moduli set {2(n) - 1, 2(n), 2(n) + 1, 2(2n-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 6n-bit DR moduli set {2(n) - 1, 2(n) + 1, 2(2n) - 2, 2(2n+1) - 3}