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New Efficient Reverse Converters for 8n-bit Dynamic Range Moduli Set

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
S. Abdul-Mumin, P. A. Agbedemnab, M. I. Daabo

S Abdul-Mumin, P A Agbedemnab and M I Daabo. New Efficient Reverse Converters for 8n-bit Dynamic Range Moduli Set. International Journal of Computer Applications 161(9):23-27, March 2017. BibTeX

	author = {S. Abdul-Mumin and P. A. Agbedemnab and M. I. Daabo},
	title = {New Efficient Reverse Converters for 8n-bit Dynamic Range Moduli Set},
	journal = {International Journal of Computer Applications},
	issue_date = {March 2017},
	volume = {161},
	number = {9},
	month = {Mar},
	year = {2017},
	issn = {0975-8887},
	pages = {23-27},
	numpages = {5},
	url = {},
	doi = {10.5120/ijca2017913243},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


This paper proposes two efficient residue to binary converters on a new three-moduli set {2^2n-1,2^4n,2^2n+1} using the Chinese Remainder Theorem. The proposed reverse converters are adder based and memoryless. In comparison with other moduli sets with similar dynamic range, the new schemes out-perform the existing schemes in terms of both hardware cost and relative performance.


  1. A. Omondi and B. Premkumar, Residue Number Systems: Theory and Implementation, vol. 2. Published By Imperial College Press And Distributed By World Scientific Publishing Co., 2007.
  2. P. A. Agbedemnab and E. K. Bankas, “A Novel RNS Overflow Detection and Correction Algorithm for the Moduli Set {2^n-1,2^n,2^n+1},” Int. J. Comput. Appl., vol. 110, no. 16, pp. 30–34, Jan. 2015.
  3. M. Bhardwaj, T. Srikanthan, and C. T. Clarke, “A reverse converter for the 4 moduli super set {2^n-1, 2^n, 2^n+1, 2^(n+1)+1},” IEEE Conf. Comput. Arith., 1999.
  4. A. Hariri, R. Rastegar, and K. Navi, “High Dyanamic Range 3-Moduli Set with Efficient Reverse Converter,” Int. J. Comput. Math. Appl.
  5. E. K. Bankas and K. A. Gbolagade, “A New Efficient FPGA Design of Residue-To-Binary Converter,” Int. J. VLSI Des. Commun. Syst. VLSICS, vol. 4, no. 6, Dec. 2013.
  6. H. Pettenghi, R. Chaves, and L. Sousa, “RNS Reverse Converters for Moduli Sets With Dynamic Ranges up to -bit,” IEEE Trans. Circuits Syst. Regul. Pap., vol. 60, no. 6, pp. 1487–1500, Jun. 2013.
  7. M. I. Daabo and K. A. Gbolagade, “RNS Overflow Detection Scheme for the Moduli set {M − 1, M},” J. Comput., vol. 4, no. 8, pp. 39–44, 2012.
  8. K. A. Gbolagade, “New Adder-Based RNS-Binary Converters for the {2^(n+1)+1,2^(n+1)-1,2^n } Moduli Set.,” Int. Sch. Res. Netw.
  9. G. Jaberipur and H. Ahmadifar, “A ROM-less reverse RNS converter for moduli set 2q ?? 1, 2q ?? 3,” IET Comput. Digit. Tech., vol. 8, no. 1, pp. 11–22, Jan. 2014.
  10. E. K. Bankas and K. A. Gbolagade, “A New Efficient RNS Reverse Converter for the 4-Moduli Set {2^n, 2^n+1, 2^n-1, 2^(2n+1)-1},” Int. J. Comput. Electr. Autom. Control Inf. Eng., vol. 8, no. 2, pp. 318–322, 2014.


Residue to binary converter, reverse converter, residue number system (RNS), Chinese remainder theorem, moduli set.