Residue-binary number conversion using signed-digit arithmetic for a three-moduli set

By introducing a signed-digit (SD) number arithmetic into a residue number system (RNS), arithmetic operations can be performed efficiently. In this paper, an algorithm of the residue to binary number conversion for a three-moduli set {2ⁿ, 2ⁿ⁺¹ - 1, 2ⁿ - 1} using the SD number arithmetic is proposed. A high speed SD addition algorithm is also presented. Based on the proposed algorithm, the converters are implemented by the SD additions in which the carry propagation is free. The design and simulation results show that fast residue-binary number converter based on the presented algorithm can be implemeted, by comparing the performance of the proposed converter with that of binary one.