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Representation & combination of Boolean functions using APL

Published: 01 June 1984 Publication History

Abstract

An ability to compactly represent and efficiently manipulate and combine Boolean functions is required in many tasks pertaining to digital logic design, including those of fault detection and isolation and the decomposition of switching networks. An APL implementation of Roth's cube array representation of Boolean functions is presented, and it is shown how such a representation permits the definition of concise and efficient APL routines to compute various useful logical combinations of these functions.

References

[1]
Dietmeyer, D.L. Logical Design of Digital Systems, Allyn & Bacon, Boston, 1971.
[2]
Iverson, K.E. "Direct Definition", SATN #36, I.P. Sharp Associates, Toronto, Ontario, Oct. 1980.
[3]
McCluskey, E.J. Introduction to the Theory of Switching Circuits, McGraw-Hill, New York, 1965.
[4]
Miller, D.M. Multiple-Valued Logic Symmetries, Unpublished Ph.D. thesis, University of Manicoba, 1976.
[5]
Mowle, F.J. A Systematic Approach to Digital Logic Design, Addison-Wesley. Mass. 1976.
[6]
Quine, W.V. "A Way to Simplify Truth Functions", Am. Math. Monthly, Vol. 62, 1955, pp. 521-531.
[7]
Reed, T.J. "APL Modeling of DeMorgan Algebras", APL79 Conference Proc., ACM, Rochester, N.Y., 1979.
[8]
Roth. J.P. "Algebraic Topologic Methods for the Synthesis of Switching Systems I", Trans. Am. Math. Soc., Vol. 88 #2, July, 1958. pp.301-326.

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cover image ACM Conferences
APL '84: Proceedings of the international conference on APL
June 1984
391 pages
ISBN:0897911377
DOI:10.1145/800058

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1984

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