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A Method of Two-Level Simplification of Boolean Functions

Published online by Cambridge University Press:  22 January 2016

Toshio Umezawa
Toshio Umezawa*
Affiliation:
Shizuoka University
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There are a number of methods to find minimal two-level forms for a given Boolean function, e g. Harvard’s group [1], Veitch [2], Quine [3], [4], Karnaugh [5], Nelson [6], [7] etc,. This paper presents an approach which is suitable for mechanical or automatic computation, as the Harvard method and the Quine method are so. On the other hand, it shares the same property as the Veitch method in the sense that some of essential prime implicants may be found before all prime implicants are computed. It also adopts the procedure to reduce the necessary steps for computation which is shown in Lawler [8]. The method described is applicable to the interval of Boolean functions f, g such that f implies g where for simplification of sum form the variables occurring in g also occur in f and for product form the variables in f also occur in g.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 201 - 210
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Staff of Harvard Computation Laboratory, Synthesis of electronic computing and control circuits, Harvard University Press, Cambridge, 1951.Google Scholar
[2] Veitch, E. W., A chart method for simplifying truth functions, Proc. Association for Computing Machinery Conference, May 2-3, 1952, pp. 127–133.Google Scholar
[3] Quine, W. V., The problem of simplifying truth-functions, Amer. Math. Monthly, 59 (1952), pp. 521–531.CrossRefGoogle Scholar
[4] Quine, W. V., A way to simplify truth functions, Amer. Math. Monthly, 62 (1955), pp. 627–631.CrossRefGoogle Scholar
[5] Karnaugh, M., The map method for synthesis of combinational logic circuits, Trans, Amer. Inst. Elec. Engrs., 72 (1) (1953), pp. 593–599.Google Scholar
[6] Nelson, R. J., Simplest normal truth functions, J. Symbolic Logic, 20 (1955), pp. 105–108.CrossRefGoogle Scholar
[7] Nelson, R. J., Weak simplest normal truth functions, J. Symbolic Logic, 20 (1955), pp. 232–234.CrossRefGoogle Scholar
[8] Lawler, E. L., An approach to multilevel Boolean minimization, J. Assoc. for Computing Machinery, 11 (1964), pp. 283–295.CrossRefGoogle Scholar
[9] Phister, M., Logical design of digital computers, John Wiley, New York, 1960.Google Scholar