Realization of an Arbitrary Switching Function with a Two-Level Network of Threshold and Parity Elements

In this short note, the realization of an arbitrary switching function by an interconnection of threshold and parity elements is considered. Using several criteria, it is shown that parity functions and threshold functions are " opposites." This dis- similarity between threshold and parity elements coupled with the useful physical properties of parity elements indicates that a realization employing the two types of modules should be of interest. Since the modules realizing parity functions are identical, mass production can be employed to reduce the cost of realization. A particular two- level configuration of threshold and parity elements is discussed. The first level consists of parity elements and the second level consists of a single threshold element. It is shown that any switching function can be realized with the proposed structure. An optimal procedure for minimizing the number of parity elements in the realization is given. Furthermore, a suboptimal procedure which is much simpler than the optimal one is also proposed.