Structure/function considerations for digital systems that contain polyfunctional elements

Abstract

This paper investigates some properties of combinational digital networks for which the elements are capable of performing many functions (mainly all the logical functions) of their input variables. Networks designed with large-scale integrated circuits such as read-only memories or programmed-logicarrays fall into this category. Central to the investigation are concepts of the universality of parts of the network, the range of functions that can be achieved by a given network, and the redundancy of some networks. On the question of range, a notation and the algebra which this implies are described. A case study is given in the Appendix to illustrate the way in which the formalisms discussed in this paper interact with intuitive design.