Further Improved Variable-Entered Karnaugh Map Procedures for Obtaining the Irredundant Forms of an Incompletely-Specified Switching Function

Abstract

Out of the potpourri of methods available for traditional minimization of switching functions, the method of the Karnaugh map is distinguished as a quick manual method that provides the user with pictorial insight. An advanced version of this map, viz., the variable- entered Karnaugh map (VEKM) doubles the variable-handling capa- bility of the map and allows its use for big Boolean algebras. The present paper offers a novel exposition of the essential features and properties of the VEKM, many of which are published for the first time. It also presents a simple and further improved VEKM procedure that obtains one of the irredundant disjunctive forms (IDFs) of an in- completely specified switching function (ISSF). Duality concepts are used to convert the present procedure into a dual one that obtains an irredundant conjunctive form for an ISSF. These procedures differ from their predecessors in two respects. First, the present procedures are rather advanced ones equipped with an explicitly stated set of rules that are clearer, though more powerful, than those of the preced- ing procedures. Second, the present procedures are more precise in handling the contributions of a map entered term, or alterm, and hence are more likely to capture minor details in the intrinsic structure of the ISSF under consideration. Therefore, the present procedures, if fol- lowed strictly, are more likely to achieve exact minimality, and even if not, the resulting expressions from them are always guaranteed to be almost minimal. Many detailed examples are given to demonstrate the essential features and properties of the map and to illustrate the rules and steps of the new procedures.