Design Of Reverse Converter Circuit For Residue Number System

Residue number system(RNS) has been widely applied in the field of encryption system and digital signal processing system due to its inherent parallelism, high speed, fault tolerant, and free-carry properties. The residue-to-binary converter, which converts the RNS-represented results into their binary weighted representations. It is one of the main factors influencing the RNS performance. In this work, three new moduli sets are proposed and their corresponding reverse converter circuits are designed:A new 4-moduli set {22n-1, 22n-1-1,2n+1,2n-1} is proposed and its corresponding reverse converter circuit is designed by using the Mixed radix conversion(MRC). Compared with the 4-moduli set with almost the same dynamic range, our converter circuit is better than the moduli set {2n-1,2n+1, 22n-2,22n+1-3} in performance. The conversion time and the circuit area are reduced by about 53.9% and 39.8%, respectively. Our converter is also better than the moduli set {22n,22n+1-1,2n+1,2n/2+1, 2n/2-1}. The conversion time and the circuit area are reduced by about 1.9% and 9.3%, respectively. Our converter is almost the same performance with that of the moduli set {2n-1,2n+1, 22 n,22n+1-1}, the conversion time and the circuit area are reduced by about2.8% and 1.8%, respectively. In addition, compared with the similar moduli set, the new 4-moduli set have better equilibrium.A new 5-moduli set {22n-1, 22n-1-1,2n+1,2n-1,2n-1-1} is achieved by actualizing lateral extension for 4-moduli set {22n-1, 22n-1-1,2n+1,2n-1}. Compared with the corresponding 4-moduli set, the reverse converter of the new 5-moduli set need add two moduli adder and a complement adder. Compared with the moduli set with almost the same dynamic range, the circuit area is reduced by about 45%, and have better modulo operations speed.In order to improve the dynamic range of moduli set, we proposed a new 8-moduli set. The reverse converter for the new 8-moduli set is based on the new Chinese remainder theorem. Compared with the moduli set with almost the same dynamic range, the new 8-moduli set has smaller resource consumption、higher parallelism、higher efficient in modulo arithmetic operations and higher equilibrium.