A New Four-Moduli Set { 22 n , 2 n / 2 – 1 , 2 n / 2 + 1 , 2 n + 1 – 1 } with an Efficient Residue to Binary Converter

Abstract

In this paper a new four-moduli set {2, 2 –1, 2 +1, 2 –1} for even n is introduced. This moduli set has 4n-bit dynamic range and well-formed moduli which can result in efficient implementation of the residue to binary converter as well as internal RNS arithmetic circuits. Then, an efficient residue to binary converter for proposed moduli set is presented. The converter for this moduli set is implemented in two-level structure which is designed based on Chinese remainder theorem (CRT) and the new CRT-I methods. The presented residue to binary converter has lower hardware cost and results in a significant reduction in the conversion delay compared to the residue to binary converter of the latest introduced four-moduli set {2n –1, 2n, 2n +1, 2n+1 –1} that has the same dynamic range as the proposed four-moduli set.

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