Data—Its Representation and Manipulation

  • John E. Hershey
  • R. K. Rao Yarlagadda
Part of the Applications of Communications Theory book series (ACTH)


In this chapter we are concerned with the preliminaries of representing information, or data, using binary units or bits. We start with a most basic concept—number systems. The number systems considered are those common ones of “normal binary representation,” negabinary, and Gray coding. We also introduce a less well known “mixed-radix system,” based on the factorials. This representation will be of use to us later on when we look at combinatorics.


Boolean Function Number System Truth Table Code Word Binary Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bitner, J., G. Ehrlich, and E. Reingold (1976), Efficient Generation of the Binary, Reflected Gray Code and Its Applications, Communications of the ACM, Vol. 19, pp. 517–521.MathSciNetMATHCrossRefGoogle Scholar
  2. Cavior, S. (1975), An Upper Bound Associated with Errors in Gray Code, IEEE Transactions on Information Theory, Vol. 21, p. 596.MathSciNetMATHCrossRefGoogle Scholar
  3. Croy, J. (1961), Rapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmetic, IRE Transactions on Electronic Computers, Vol. 10, p. 777.Google Scholar
  4. Karpovsky, M. (1976), Finite Orthogonal Series in the Design of Digital Devices, Wiley, New York.MATHGoogle Scholar
  5. Rothaus, O. (1976), On “Bent” Functions, Journal of Combinatorial Theory, Series A, Vol. 20, No. 3, May.Google Scholar
  6. Sellers, F., M-Y. Hsiao, and L. Bearnson (1968), Error Detecting Logic for Digital Computers, McGraw-Hill, New York.Google Scholar
  7. Titsworth, R. (1964), Optimal Ranging Codes, IEEE Transactions on Space Electronics and Telemetry, pp. 19–30, March.Google Scholar
  8. Wadel, L. (1961), Conversion from Conventional to Negative-Base Number Representation, IRE Transactions on Electronic Computers, p. 779.Google Scholar
  9. Wang, M. (1966), An Algorithm for Gray-to-Binary Conversion, IEEE Transactions on Electronic Computers, pp. 659–660.Google Scholar
  10. Yates, F. (1937), The Design and Analysis of Factorial Experiments, Imperial Bureau of Soil Science, Harpenden, England.Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • John E. Hershey
    • 1
  • R. K. Rao Yarlagadda
    • 2
  1. 1.The BDM CorporationBoulderUSA
  2. 2.Oklahoma State UniversityStillwaterUSA

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