An Efficient FPGA Design of Residue-to-Binary Converter for the Moduli Set ${2n+1,2n,2n-1}$

In this paper, we propose a novel reverse converter for the moduli set {2n+1,2n,2n-1}. First, we simplify the Chinese Remainder Theorem in order to obtain a reverse converter that uses mod-(2n-1) operations. Next, we present a low complexity implementation that does not require the explicit use of modulo operation in the conversion process and we prove that theoretically speaking it outperforms state of the art equivalent converters. We also implemented the proposed converter and the best equivalent state of the art converters on Xilinx Spartan 3 field-programmable gate array. The results indicate that, on average, our proposal is about 14%, 21%, and 8% better in terms of conversion time, area cost, and power consumption, respectively.