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Modulo Operation Free Reverse Conversion in the {2^(2n+1)-1,2^n,2^2n-1} Moduli Set

by H. Siewobr, K. A. Gbolagade
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 85 - Number 18
Year of Publication: 2014
Authors: H. Siewobr, K. A. Gbolagade
10.5120/14939-2911

H. Siewobr, K. A. Gbolagade . Modulo Operation Free Reverse Conversion in the {2^(2n+1)-1,2^n,2^2n-1} Moduli Set. International Journal of Computer Applications. 85, 18 ( January 2014), 6-14. DOI=10.5120/14939-2911

@article{ 10.5120/14939-2911,
author = { H. Siewobr, K. A. Gbolagade },
title = { Modulo Operation Free Reverse Conversion in the {2^(2n+1)-1,2^n,2^2n-1} Moduli Set },
journal = { International Journal of Computer Applications },
issue_date = { January 2014 },
volume = { 85 },
number = { 18 },
month = { January },
year = { 2014 },
issn = { 0975-8887 },
pages = { 6-14 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume85/number18/14939-2911/ },
doi = { 10.5120/14939-2911 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:02:46.773973+05:30
%A H. Siewobr
%A K. A. Gbolagade
%T Modulo Operation Free Reverse Conversion in the {2^(2n+1)-1,2^n,2^2n-1} Moduli Set
%J International Journal of Computer Applications
%@ 0975-8887
%V 85
%N 18
%P 6-14
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper proposes a fast Mixed Radix Conversion based reverse converter for the recently proposed moduli set ?{2?^(2n+1)-1,2^n,2^2n-1}. It shows that the computation of multiplicative inverses could be eliminated from the conversion process and presents a low complexity and modulo operation free implementation. Theoretical analysis shows that the proposed scheme outperforms all state of the art equivalent converters in terms of both area cost and delay.

References
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  2. A. P. Vinod and A. B. Premkumar, A memoryless residue to binary converter for the 4-superset ?" {2" ?^"n" "-1," "2" ^"n" "," ?"2" ^"n" "+1,2" ?^"n+1" "-1}" , Journal of Circuits, Syst. and Computers, Vol. 10, pp. 85-99,2000.
  3. K. A. Gbolagade and S. D. Cotofana, MRC Technique for RNS to Decimal Conversion for the Moduli Set "{2n + 2,2n + 1,2n}" , 16th Annual Workshop on Circuits, Systems, and Signal Processing, pp. 318-321, Veldhoven, The Netherlands, November, 2008.
  4. K. A. Gbolagade, G. R. Voicu, and S. D. Cotofana, An Efficient FPGA Design of Reverse Converter for the Moduli Set"{2n + 2,2n + 1,2n}" , 5th International Summer School on Advanced Computer Architecture and Compilation for Embedded Systems(ACACES 2010), pp. 117-120, Terrassa, Spain, July 11-17, 2010.
  5. A. S. Molahosseini, K. Navi, C. Dadkhah, O. Kavehei, S. Timarchi, Efficient Reverse Converter Designs for the New 4-Moduli Sets ? {2?^n-1,2^n,2^n+1 ?,2?^(2n+1)-1} and ? {2?^n-1,2^n+1 ?,2^2n,2?^(2n+1)-1} Based on New CRTs, IEEE Trans. Circuits and Systems-I, vol. 57, pp. 823, Apr2010.
  6. Leonel Sousa, Samuel Antao, MRC-Based RNS reverse converters for the Four-Moduli sets ? {2^n+1 ,2?^n-1,2^n ?,2?^(2n+1)-1} and ? {2^n+1 ,2?^n-1,2^2n ?,2?^(2n+1)-1}, IEEE Transactions on Circuits and Systems 59-II (4), pp. 244-248, 2012.
  7. K. A. Gbolagade, R. Chaves, L. Sousa, and S. D. Cotofana, An Improved RNS Reverse Converter for the ?"{2" ?^"2n+1" "-1," ?"2" ^"n" ",2" ?^"n" "-1}" Moduli Set, IEEE International Symposium on Circuits and Systems (ISCAS2010), pp. 2103-2106, Paris, France, June, 2010.
  8. K. A. Gbolagade, An Efficient MRC based RNS-to-Binary Converter for the ?{2?^(2n+1)-1,2^n,2^2n-1} moduli set, AIMS SA, 2011.
  9. K. A. Gbolagade and S. D. Cotofana, An O(n) Residue Number System to Mixed Radix Technique, IEEE International Symposium on Circuits and Systems (ISCAS 2009), pp. 521-524, Taipei, Taiwan, China, May, 2009.
Index Terms

Computer Science
Information Sciences

Keywords

Reverse Conversion Mixed Radix Conversion Moduli Set Multiplicative Inverses.

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