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The Characterization and Properties of Cascade Realizable Switching Functions
July 1969 (vol. 18 no. 7)
pp. 624-633
C.D. Weiss, IEEE
This paper is a study of switching functions realizable by a single cascaded switching network composed of two-input, one-output elements where a distinct variable is applied to one input and the other receives the output of the previous element. A special type of Boolean formula called a standard cascade form is introduced with the property that all cascade realizable functions, and only these, can be written in this form. This characterization leads to a strong necessary condition on such functions: there is no consensus for any pair of its prime implicants which are, therefore, all core. It also leads to a new, efficient procedure for testing an arbitrary function f for cascade realizability. The test operates on the prime implicants of f, and yields a realization employing a particular complete set of cell types from which it is especially easy to derive any other realization using any other complete set.
Index Terms:
Arrays of cascades, Boolean formula, cascaded switching networks, core prime implicants, optimal realization, prime implicants, standard cascade form, switching functions, two-input one-output elements.
Citation:
C.D. Weiss, "The Characterization and Properties of Cascade Realizable Switching Functions," IEEE Transactions on Computers, vol. 18, no. 7, pp. 624-633, July 1969, doi:10.1109/T-C.1969.222729
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