Theory of Extended Forms of Switching Function

Abstract

In switching algebra, there exist standard forms of Boolean functions such as the disjunctive or conjunctive form. This paper discusses the theory of the extended standard forms of Boolean functions. In addition to the four existing standard forms, two further forms are introduced and thus expanded to six basic forms. On the one hand, the existence of the extended forms is presented and on the other hand new formulas and equations are illustrated. Equations relating to the resolution and/or solution of conjunction/disjunctions are detailed and proven to be valid. In addition, equations for conversion between forms are exemplified. Finally, certain formal relations between the basic forms that are valid under certain conditions are featured.