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Data—Its Representation and Manipulation

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Part of the book series: Applications of Communications Theory ((ACTH))

Abstract

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.

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References

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Cavior, S. (1975), An Upper Bound Associated with Errors in Gray Code, IEEE Transactions on Information Theory, Vol. 21, p. 596.

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  • 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.

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  • Karpovsky, M. (1976), Finite Orthogonal Series in the Design of Digital Devices, Wiley, New York.

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  • Rothaus, O. (1976), On “Bent” Functions, Journal of Combinatorial Theory, Series A, Vol. 20, No. 3, May.

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  • Sellers, F., M-Y. Hsiao, and L. Bearnson (1968), Error Detecting Logic for Digital Computers, McGraw-Hill, New York.

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  • Titsworth, R. (1964), Optimal Ranging Codes, IEEE Transactions on Space Electronics and Telemetry, pp. 19–30, March.

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  • Wadel, L. (1961), Conversion from Conventional to Negative-Base Number Representation, IRE Transactions on Electronic Computers, p. 779.

    Google Scholar 

  • Wang, M. (1966), An Algorithm for Gray-to-Binary Conversion, IEEE Transactions on Electronic Computers, pp. 659–660.

    Google Scholar 

  • Yates, F. (1937), The Design and Analysis of Factorial Experiments, Imperial Bureau of Soil Science, Harpenden, England.

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© 1986 Plenum Press, New York

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Hershey, J.E., Rao Yarlagadda, R.K. (1986). Data—Its Representation and Manipulation. In: Data Transportation and Protection. Applications of Communications Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2195-8_1

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  • DOI: https://doi.org/10.1007/978-1-4613-2195-8_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9290-6

  • Online ISBN: 978-1-4613-2195-8

  • eBook Packages: Springer Book Archive

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