Abstract
In the process of finding a minimal sum representation for an incompletely specified multiple-output switching function, there often occur certain types of prime implicants, referred to as useless, which can be discarded because of the presence of the “don't-cares.” This paper presents a correction to the definition of useless given by Tison and extends the definition to other notations. A procedure for removing useless prime implicants quickly is presented for the case when multiple-output prime implicants are derived from minterms. The deletion of useless prime implicants can, in many cases, speed up any procedure for finding a minimal sum that begins with the multiple-output prime implicants in both hand calculation and in computer implementation.
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References
P. Tison, “Generalization of consensus theory and application to the minimization of Boolean functions,”IEEE Trans. Electronic Comprs EC-16:446–456 (August 1967).
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This work was supported in part by the National Science Foundation under Grant No. MCS-77-09744.
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Cutler, R.B., Muroga, S. Useless prime implicants of incompletely specified multiple-output switching functions. International Journal of Computer and Information Sciences 9, 337–350 (1980). https://doi.org/10.1007/BF00978165
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DOI: https://doi.org/10.1007/BF00978165