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Introduction

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Residue Number Systems

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Abstract

Digital computation is carried out using binary number system conventionally. Processors with word lengths up to 64 bits have been quite common. Several number systems have been investigated in the past for realizing processors for arithmetic as well as signal processing applications. These are decimal number system, binary number system, Mixed Radix Number system, Logarithmic Number System and Residue Number System. In this chapter we briefly present these and give a historical introduction to the main topic of this book- Residue Number Systems.

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References

  1. M.G. Arnold, The residue logarithmic number system: Theory and application, in Proceedings of the 17th IEEE Symposium on Computer Arithmetic (ARITH), Cape Cod, 27–29 June 2005, pp. 196–205

    Google Scholar 

  2. E.C. Ifeachor, B.W. Jervis, Digital Signal Processing: A Practical Approach, 2nd edn. (Pearson Education, Harlow, 2003)

    Google Scholar 

  3. I. Koren, Computer Arithmetic Algorithms (Brookside Court, Amherst, 1998)

    MATH  Google Scholar 

  4. S.W. Smith, The Scientists’s and Engine’s Guide to Digital Signal Processing (California Technical, San Diego, 1997). Analog Devices

    Google Scholar 

  5. T. Stouraitis, V. Paliouras, Considering the alternatives in low power design. IEEE Circuits Devic. 17(4), 23–29 (2001)

    Google Scholar 

  6. F.J. Taylor, A 20 bit logarithmic number system processor. IEEE Trans. Comput. C-37, 190–199 (1988)

    Article  Google Scholar 

  7. L.K. Yu, D.M. Lewis, A 30-bit integrated logarithmic number system processor. IEEE J. Solid State Circuits 26, 1433–1440 (1991)

    Article  Google Scholar 

  8. J.R. Sacha, M.J. Irwin, The logarithmic number system for strength reduction in adaptive filtering, in Proceedings of the International Symposium on Low-power Electronics and Design (ISLPED98), Monterey, 10–12 Aug. 1998, pp. 256–261

    Google Scholar 

  9. V. Paliouras, T. Stouraitis, Low power properties of the logarithmic number system, in 15th IEEE Symposium on Computer Arithmetic, Vail, 11–13 June 2001, pp. 229–236

    Google Scholar 

  10. H. Garner, The residue number system. IRE Trans. Electron. Comput. 8, 140–147 (1959)

    Article  Google Scholar 

  11. F.J. Taylor, Residue arithmetic: A tutorial with examples. IEEE Computer 17, 50–62 (1984)

    Article  Google Scholar 

  12. C.F. Gauss, Disquisitiones Arithmeticae (1801, English translation by Arthur A. Clarke). (Springer, New York, 1986)

    Google Scholar 

  13. S. Kak, Computational aspects of the Aryabhata algorithm. Indian J. Hist. Sci. 211, 62–71 (1986)

    MathSciNet  MATH  Google Scholar 

  14. W.E. Clark, The Aryahbatiya of Aryabhata (University of Chicago Press, Chicago, 1930)

    Google Scholar 

  15. K.S. Shulka, K.V. Sarma, Aryabhateeya of Aryabhata (Indian National Science Academy, New Delhi, 1980)

    Google Scholar 

  16. T.R.N. Rao, C.-H. Yang, Aryabhata remainder theorem: Relevance to public-key Crypto-algorithms. Circuits Syst. and Signal. Process. 25(1), 1–15 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. J.H. Yang, C.C. Chang, Aryabhata remainder theorem for Moduli with common factors and its application to information protection systems, in Proceedings of the International Conference on Intelligent Information Hiding and Multimedia Signal Processing, Harbin, 15–17 Aug. 2008, pp. 1379–1382

    Google Scholar 

  18. W.A. Chren, One-hot residue coding for low delay-power product CMOS designs. IEEE Trans. Circuits Syst. 45, 303–313 (1998)

    Article  Google Scholar 

  19. Q. Ke, M.J. Feldman, Single flux quantum circuits using the residue number system. IEEE Trans. Appl. Supercond. 5, 2988–2991 (1995)

    Article  Google Scholar 

  20. C.D. Capps et al., Optical arithmetic/logic unit based on residue arithmetic and symbolic substitution. Appl. Opt. 27, 1682–1686 (1988)

    Article  Google Scholar 

  21. N. Szabo, R. Tanaka, Residue Arithmetic and Its Applications in Computer Technology (McGraw Hill, New York, 1967)

    MATH  Google Scholar 

  22. R.W. Watson, C.W. Hastings, Residue Arithmetic and Reliable Computer Design (Spartan, Washington, DC, 1967)

    Google Scholar 

  23. M.A. Soderstrand, G.A. Jullien, W.K. Jenkins, F. Taylor (eds.), Residue Number System Arithmetic: Modern Applications in Digital Signal Processing (IEEE Press, New York, 1986)

    Google Scholar 

  24. P.V. Ananda Mohan, Residue Number Systems: Algorithms and Architectures (Kluwer, Boston, 2002)

    Book  Google Scholar 

  25. A.R. Omondi, B. Premkumar, Residue Number Systems: Theory and Implementation (Imperial College Press, London, 2007)

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. R&D, CDAC, Bangalore, Karnataka, India

    P. V. Ananda Mohan

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  1. P. V. Ananda Mohan
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Ananda Mohan, P.V. (2016). Introduction. In: Residue Number Systems. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-41385-3_1

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