International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

An Efficient Residue to Binary Converter for the New Two-Level Moduli Set {22n {2n ,2n+1 -1},2n -1, 2n + 1}

Author Affiliations

  • 1 Department of Computer Engineering, Ahvaz branch, Islamic Azad University, Ahvaz, IRAN
  • 2 Department of Computer Engineering, Ahvaz branch, Islamic Azad University, Shoushtar, IRAN
  • 3
  • 4
  • 5

Res. J. Recent Sci., Volume 1, Issue (7), Pages 83-86, July,2 (2012)


In this paper a new two-level four moduli set {22n {2n ,2n+1 -1},2n -1, 2n + 1} is introduced and an efficient residue to binary converter is proposed for it. This moduli set contains the moduli set {22n, 2n 1, 2n +1} in its first-level and the moduli set {2, n+1 1} in its second-level for the modulo 22n.The reverse converter for this moduli set is implemented in two-level structure, which is designed based on Chinese remainder theorem (CRT) and the new CRT-1 methods. The proposed residue to binary converter for this moduli set improves the hardware cost and delay significantly in comparison to the similar previously presented moduli sets.


  1. Omondi A. and Premkumar B., Residue Number Systems:Theory and Implementations, Imperial College Press, London (2007)
  2. Mohan P.V.A., RNS-To-Binary Converter for a New Three-moduli Set {2n+1 1,2n ,2 1} , IEEE trans. Circuits Syst., 54(9), 775-779 (2007)
  3. Sabbagh A., Dadkhah C.H., Navi K. and Eshghi M., Efficient MRC-Based Residue to Binary Converters for the New Moduli Sets {22n,2 1,2n+1 1} and {22n,2 1,2n1 1}, IEICE TRANS. INF. & SYST., 92(9), 42-51 (2009)
  4. Hariri A., Navi K. and Restegar R., A new high dynamic range moduli set with efficient reverse converter, Elsevier J. com and Math, 55(4), 660-668 (2008)
  5. Mohan P.V.A. and Premkumar A.B., RNS-to-Binary Converters for Two Four-Moduli Set {2 1,2n ,2 +1,2n+11} and {2 1,2,2 +1,2n+1+1}, IEEE Trans. Circuits syst. I, 54(6), 1245-1254 (2007)
  6. Mohan P. V. A., New reverse converters for the moduli set {2 3,2 1,2+1 ,2+3}, Elsevier J. Electron. Commun., 62(9), 643-658 (2008)
  7. Hosseinzadeh M., Sabbagh A. and Navi K., An improved reverse converter for the moduli set {2 1, 2, 2 +1, 2n+1 1}, IEICE Elect. Exp, 5(17), 672-677 (2008)
  8. Mewada Shivlal and Singh Umesh Kumar, Performance Analysis of Secure Wireless Mesh Networks, Researh J. Recent Sci.,1(3), 80-85 (2012)
  9. Molahosseini A., Navi K., Hashemipour O. and A. Jalali, An efficient architecture for designing reverse converters based on a general three moduli set, Elsevier J. Systems Architecture, 54(10), 929-934 (2008)
  10. Wang W., Swamy M. N. S., Ahmad M. O. and Wang Y., A Study of the Residue-to-Binary Converters for the Three-Moduli Sets, IEEE Trans. Circuits and Syst-II, 40(2), 235-243 (2003)
  11. Piestrak S.J., A high speed realization of a residue to binary converter, IEEE Trans. Circuits and Syst-II, 42(10), 661-663 (1995)