Extended Forms of Switching Functions

Two new extended forms of switching functions with the four already existing forms, which will be partly renamed, are presented in this paper. These new extended forms, the antivalence of disjunctions ADF and the equivalence of conjunctions EcF, are educed from circuit of digital logic gates and thereby their algebraic expressions are set up. For that, conversion rules which enable the transformation of a disjunction in equivalence-operation and the transformation of a conjunction in antivalence-operation with respect to the extended forms will be lay down. In addition, new formulas for resolution of terms of ADF and EcF while retaining the form of the given function will be derived. Furthermore, relations between these six forms are described in algebra of sets if they have the same representation of disjunctions respectively conjunctions whereby the conjunctions and disjunctions have operations of the same literals. Additionally, in the case of orthogonal representation of these six function forms further relations between them result. That means, an orthogonal disjunctive form is equivalent to the orthogonal antivalence form of conjunctions and equivalent to the complement of the orthogonal equivalence form of conjunctions. Against this, an orthogonal conjunctive form is equivalent to the orthogonal antivalence form of disjunctions and equivalent to the complement of the orthogonal equivalence form of disjunctions.