Skip to main content

Number Systems and Number Representations

  • Chapter
  • 33 Accesses

Abstract

The familiar decimal system is by no means the only possible number system. Considered impartially, it merely constitutes one among possible and practical systems which became propagated, probably for the sole reason that human beings happen to have ten fingers. The Mayas used the vigesimal number system (based upon 20, i.e. fingers and toes) [1] and even in our days, there are some endeavors to introduce the duodecimal system (based on 12) for general use [2]. Since computers are not bound by tradition and since the decimal system has no unique merits, the designer of a computer is free to select that number system which suits his purpose best.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ceram C. W.: Gods, Graves, and Scholars. New York: Alfred A. Knopf. 1952.

    Google Scholar 

  2. Terry G. S.: The Dozen-System. London, New York, Toronto: Longmans, Green & Co. 1941.

    MATH  Google Scholar 

  3. Duodecimal Bulletin of the Duodecimal Society of America. 20, Carlton Place. Staten Island. N.Y.

    Google Scholar 

  4. White G. S.: Coded Decimal Number Systems for Digital Computers, Proceedings IRE, vol. 41, No. 10, pp. 1450–1452. Oct. 1953.

    Google Scholar 

  5. Hamming R. W.: Error Detecting and Error Correcting Codes, Bell System Technical Journal, vol. 29, pp. 147–160. Apr. 1950.

    MathSciNet  Google Scholar 

  6. Reed I. S.: A Class of Multiple-Error-Correcting Codes and the Decoding Scheme, 1954 Symposium on Information Theory, Transactions IRE, vol. IT-4, pp. 38–49. Sept. 1954.

    Google Scholar 

  7. Ulrich W.: Non-Binary Error Correction Codes, Bell System Technical Journal, vol. 36, No. 6, pp. 1341–1382. Nov. 1957.

    MathSciNet  Google Scholar 

  8. Garner H. L.: Generalized Parity Checking, Transactions IRE, vol. EC-7, No. 3, pp. 207–213. Sept. 1958.

    MathSciNet  Google Scholar 

  9. Kilmer W. L.: An Idealized Over-All Error Correcting Digital Computer, etc., Transactions IRE, vol. EC-8, No. 3, pp. 321–325. Sept. 1959.

    Google Scholar 

  10. Brown D. T.: Error Detecting and Correcting Binary Codes for Arithmetic Operations, Transactions IRE, vol. EC-9, No. 3, pp. 333–337. Sept. 1960.

    Google Scholar 

  11. Peterson, and Brown: Cyclic Codes for Error Detection, Proceedings IRE, vol. 49, No. 1, pp. 228–235. Jan. 1961.

    MathSciNet  Google Scholar 

  12. Marcus M. P.: Minimum Polarized Distance Codes, IBM Journal of Research and Development, vol. 5, No. 3, pp. 241–248. July 1961.

    MATH  Google Scholar 

  13. Gorog E.: Some New Classes of Cyclic Codes Used for Burst-Error Correction, IBM Journal of Research and Development, vol. 7, No. 2, pp. 102–111. Apr. 1963.

    MATH  Google Scholar 

  14. Garner H. L.: The Residue Number System, Transactions IRE, vol. EC-8. No. 2, pp. 140–147. June 1959.

    Google Scholar 

  15. Guffin R. M.: A Computer... Using the Residue Number System, Transactions IRE, vol. EC-11, No. 2, pp. 164–173. Apr. 1962.

    MathSciNet  Google Scholar 

  16. Szabo N.: Sign Detection in Nonredundant Residue Systems, Transactions IRE, vol. EC-11, No. 4, pp. 494–500. Aug. 1962.

    Google Scholar 

  17. Keir, Cheney, and Tannenbaum: Division and Overflow Detection in Residue Number Systems, Transactions IRE, vol. EC-11, No. 4, pp. 501–507. Aug. 1962.

    MathSciNet  Google Scholar 

  18. Merrill R. D.: Improving Digital Computer Performance Using Residue Number Theory, Transactions IRE, vol. EC-13, No. 2, pp. 93–101. Apr. 1964.

    MATH  Google Scholar 

  19. Songster G. F.: Negative-Base Number-Representation Systems, Transactions IEEE, vol. EC-12, No. 3, pp. 274–277. June 1963.

    MATH  Google Scholar 

  20. Lippel B.: Negative-Bit Weight Codes and Excess Codes, Transactions IEEE, vol, EC-13, No. 3, pp. 304–306. June 1964.

    Google Scholar 

Selected Bibliography

  • Dickson L. E.: Modern Elementary Theory of Numbers. Chicago: University of Chicago Press. 1939.

    Google Scholar 

  • Staff of Engineering Research Associates, High-Speed Computing Devices. New York: McGraw-Hill. 1950.

    Google Scholar 

  • Richards R. K.: Arithmetic Operations in Digital Computers. Princeton: D. Van Nostrand. 1955.

    Google Scholar 

  • Hard Y, and Wright: An Introduction to the Theory of Numbers. London: Oxford University Press. 1956.

    Google Scholar 

  • Mccracken D. D.: Digital Computer Programming. New York: John Wiley and Sons. 1957.

    MATH  Google Scholar 

  • Crowder N. A.: The Arithmetic of Computers. New York: Doubleday & Co. 1960. (A “Tutor Text”.)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1967 Springer-Verlag Wien

About this chapter

Cite this chapter

Gschwind, H.W. (1967). Number Systems and Number Representations. In: Design of Digital Computers. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3369-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-3369-9_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-3370-5

  • Online ISBN: 978-3-7091-3369-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics