A status review of incorporation of facts efficient and optimized residue to binary converter for the moduli set {2n,22n-1-1,22n-2-1} based on MRC algorithm

Abstract EN

Residue number system supports high speed and parallel arithmetic due to some special features such as limited carry-on propagation.

One of the most important issues in RNS is selecting appropriate moduli sets because it has direct effect on representation range, number of locations for numbers representation, speed of internal arithmetic, reverse converter designing, complexity of circuits and their corresponding hardware.

In this paper a novel moduli set {2n, 22n-1, -1, 22n-2-1} is proposed.

This moduli set has 5n-bits dynamic range and consists of simple and well-formed modulus which results in efficient residue to binary converter and internal arithmetic circuits for RNS.

Afterward, an efficient residue to binary converter is presented for this new moduli set based on mixed-radix theorem.

The proposed converter improves the delay and hardware cost in comparison to other 5n-bits dynamic range moduli sets significantly.