Skip to main content
SpringerLink
Log in

Efficient CRT-based residue-to-binary converter for the arbitrary moduli set

  • Research Papers
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

The conversion from residue to weighted binary representation plays an important role in the residue number system. Based on Chinese Remainder Theorem, a new residue-to-binary converter using arbitrary moduli set is proposed. The new converter uses the difference-correction algorithm for the conversion output and eliminates the modulo M operation, where M is the dynamic range of the residue number system. The sizes of the multipliers and modular multipliers in the new converter are small, thereby reducing the area and delay of the proposed converter. Simulation and synthesis results indicate that the new converter is more area-time efficient than the published converters based on Chinese Remainder Theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Szabo N S, Tanaka R I. Residue Arithmetic and Its Applications to Computer Technology. New York: McGraw-Hill, 1967

    MATH  Google Scholar 

  2. Taylor F J. Residue arithmetic: a tutorial with examples. IEEE Comput, 1984, 17: 50–62

    Google Scholar 

  3. Beame P W, Cook S A, Hoover H J. Log depth circuits for division and related problems. SIAM J Comput, 1986, 15: 994–1003

    Article  MATH  MathSciNet  Google Scholar 

  4. Soderstrand M A, Jenkins W K, Jullien G A, et al. Residue Number System Arithmetic: Modern Applications in Digital Signal Processing. New York: IEEE Press, 1986

    MATH  Google Scholar 

  5. Leighton T. Introduction to Parallel Algorithms and Architectures: Array, Trees, Hypercubes. San Mateo, CA: Morgan Kaufmann, 1992

    Google Scholar 

  6. Lim K P, Premkumar A B. A modular approach to the computation of convolution sum using distributed arithmetic principles. IEEE Trans Circuits Syst II, 1999, 46: 92–96

    Article  MATH  Google Scholar 

  7. Koren I. Computer Arithmetic Algorithms. 2nd ed. Massachusetts: AK Peters Natick, 2002

    MATH  Google Scholar 

  8. Ma S, Hu J H, Zhang L, et al. An efficient RNS parity checker for moduli set 2n − 1, 2n + 1, 22n + 1 and its applications. Sci China Ser F-Inf Sci, 2008, 51: 1563–1571

    Article  MATH  MathSciNet  Google Scholar 

  9. Wang Y K. Residue-to-binary converters based on new Chinese remainder theorems. IEEE Trans Circuits Syst II, 2000, 47: 197–205

    Article  MATH  Google Scholar 

  10. Hariri A, Navi K, Rastegar R. A new high dynamic range moduli set with efficient reverse converter. Comput Math Appl, 2008, 55: 660–668

    Article  MATH  MathSciNet  Google Scholar 

  11. Cao B, Chang C H, Srikanthan. A residue-to-binary converter for a new five-moduli set. IEEE Trans Circuits Syst I, 2007, 54: 1041–1049

    Article  MathSciNet  Google Scholar 

  12. Wang W, Swamy M, Ahmad M. A high-speed residue-to-binary converter for three-moduli (2k, 2k − 1, 2k−1 − 1) RNS and a scheme for its VLSI implementation. IEEE Trans Circuits Syst II, 2000, 47: 1576–1581

    Article  MATH  Google Scholar 

  13. Al-Radadi E, Siy P. Four-moduli set (2, 2n − 1, 2n + 2n − 1 − 1, 2n+1 + 2n − 1) simplifies the residue to binary converters based on CRT II. Comput Math Appl, 2002, 44: 1581–1587

    Article  MATH  MathSciNet  Google Scholar 

  14. Mohan P V A, Premkumar A B. RNS-to-binary converters for two four-moduli sets 2n − 1, 2n, 2n + 1, 2n+1 − 1 and 2n − 1, 2n, 2n + 1, 2n+1 + 1. IEEE Trans Circuits Syst I, 2007, 54: 1245–1254

    Article  MathSciNet  Google Scholar 

  15. Lu M, Chiang J. A novel division algorithm for the residue number system. IEEE Trans Comput, 1992, 41: 1026–1032

    Article  MathSciNet  Google Scholar 

  16. Dimauro G, Impdedovo S, Pirlo G. A new technique for fast number comparison in the residue number systems. IEEE Trans Comput, 1993, 42: 608–612

    Article  MathSciNet  Google Scholar 

  17. Conway R, Nelson J. New CRT-based RNS converter using restricted moduli set. IEEE Trans Comput, 2003, 52: 572–578

    Article  Google Scholar 

  18. Meehan S, O’neil S, Vaccaro J. An universal input and output RNS converter. IEEE Trans Circuits Syst, 1990, 37: 799–803

    Article  Google Scholar 

  19. Deng M J, Tan Y H, Sun Y Q. The Foundation of Number Theory. Harbin: Harbin Publishing House, 2000

    Google Scholar 

  20. Zhang C N, Shirazi B, Yun D. An efficient algorithm and parallel implementations for binary and residue number systems. J Symb Comput, 1993, 15: 451–462

    Article  MATH  MathSciNet  Google Scholar 

  21. Elleithy K, Bayoumi M. Fast and flexible architectures for RNS arithmetic decoding. IEEE Trans Circuits Syst, 1992, 39: 226–235

    Article  MATH  Google Scholar 

  22. Kim J, Park K, Lee H. Efficient residue-to-binary conversion technique with rounding error compensation. IEEE Trans Circuits Syst, 1991, 38: 315–317

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou, 510640, China

    JianWen Chen & RuoHe Yao

Authors
  1. JianWen Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. RuoHe Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to RuoHe Yao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, J., Yao, R. Efficient CRT-based residue-to-binary converter for the arbitrary moduli set. Sci. China Inf. Sci. 54, 70–78 (2011). https://doi.org/10.1007/s11432-010-4133-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-010-4133-3

Keywords

Search

Navigation