Computer Minimization of Multivalued Switching Functions

Abstract

A cubical representation for multivalued switching functions, which is very convenient for digital computer processing, is presented. A p-valued switching function of n variables is represented by an array of cubes. Each cube is composed of a logical co-efficient and n coordinates with each coordinate represented by p bits. A set of operators for multivalued logic design (such as sharp, union, etc.) for manipulating arrays of cubes is defined and used for minimizing multivalued switching functions. The idea of ``compound literals'' is introduced, which yields a realization with less hardware than the existing methods. Algorithms for finding all prime implicants, essential prime implicants, and a near-minimum cover for multivalued switching functions are presented that are suitable for both computer and hand execution. These algorithms have been programmed in Fortran.