An Approach to Unified Methodology of Combinational Switching Circuits

A methodology based on the theory of Boolean equations has been developed which permits a unified approach to the analysis and synthesis of combinational logic circuits. The type of circuits covered by the approach includes both the classical loopless combinational networks as well as those that contain closed feedback loops and thus have internally a sequential character. To that end, a general multiple-output circuit represented by a Mealy-type machine is studied using characteristic equations (functions) that describe its internal structure. It is shown how behavioral properties of the circuit are reflected through the sosutions of these equations. Moreover, it is demonstrated that a multiple-output incompletely specified switching function is reaeized if a ≤ relation is satisfied between the corresponding charchteristic functions. This leads to a new unified outlook on functional decomposition as used in modular synthesis procedures. Although the building modules are allowed to be sequential circuits, it is shown under which conditions the feedback loops are redundant with respect to the realization of a given output characteristic function, and thus the existence conditions of nondegenerate combinational circuits with loops are stated.