VLSI Implementation of an Efficient Residue-to-Binary Converter for the New Moduli Set {22n+1 -1,22n,2n+1-1}

Author (s):

  1. Hillary Siewobr, University for Development Studies, Navrongo, Ghana, siewobrministry@gmail.com
  2. K. A. Gbolagade, University for Development Studies, Navrongo, Ghana

Abstract:

In this paper, we present the new moduli set {22n+1 -1,22n,2n+1-1} for Residue Number System. Consequently, a residue to binary converter for this moduli set is proposed based on mixed radix conversion technique. We show that, the computation of multiplicative inverses could be avoided since they are either unity or powers of and present a low complexity converter that does not require the explicit use of modulo operations as opposed to mods- 22n-1,22n+1, and 24n-1 required by the state of the art. The proposed converter and the state of the art converters are implemented on Xilinx Xc4vlx15-10sf363 FPGA. The implementation results suggest that, on the average, the converter for the proposed moduli set {22n+1 -1,22n,2n+1-1} improves area and delay required by the state of the art converter for the moduli set {2n -1,2n,2n+1, 22n+1-1} by about and respectively and also improves the area and delay required by the state of the art converter for the moduli set {2n -1,2n,2n+1, 22n+1+1} by about 53.0.% and 32.40% respectively.

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