Variable-entered Karnaugh Map Procedures for Obtaining the Irredundant Disjunctive Forms of a Switching Function from Its Complete Sum

Abstract

The covering problem, a classical problem in switching theory, involves the selection of some prime implicants irredundantly to cover the asserted part of an incompletely specified switching function. This paper advocates the use of the variable-entered Karnaugh map (VEKM) to solve this problem. To set the stage for achieving this purpose, a novel tutorial exposition of the VEKM-related variable-entered cover matrix is presented. Subsequently, the paper offers two VEKM solutions of the covering problem. The first solution relies on the new concept of VEKM loops. By contrast to a loop on a conventional Karnaugh map which is characterized by a single product, a VEKM loop is identified by two products, namely loop coverage (which depends only on map variables) and loop depth (which depends only on entered variables). In the second solution, the VEKM is used directly as a cover map in such a way that it is not littered with unnecessary details or too many overlapping loops. All solution procedures are demonstrated via illustrative examples that help reveal their visual merits as well as their applicability to relatively large problems.