Cascaded Switching Networks of Two-Input Flexible Cells

This paper studies a class of switching networks which are constructed by cascading two-input, single-output completely flexible binary logical cells. It is assumed that each cell can be adjusted at will in order that any one of the sixteen possible switching functions of its two binary inputs may be obtained at its single output lead. An n-input cascaded network is composed of n-l, two-input, single output logical cells. The inputs to a typical cell Ai consist of a signal variable Xi and the output ai from the preceding cell Ai-1. For the end cell A1 the inputs are the signal variables X0 and X1. The output is derived from the terminal cell An-1. In view of the growing interest in the area of ``self-organizing'' or ``adaptive'' switching networks, the study of the type of network just discussed seems to be pertinent. The results presented here are pertinent to typical n-input cascaded structures, and consist of characterization and enumeration of the class of all n-place realizable switching functions, test procedure for the determination of the realizability of arbitrary n-place switching functions, and finally determination of all possible cascaded structures for synthesis of realizable n-place switching functions. The paper develops some new techniques especially suited to the present study. These techniques may also hopefully find applications in other types of logic synthesis.