Basis forms of switching functions an their orthogonal relation

This paper presents extended forms, equations, and relationships of switching function which are derived out of the theoretical handling of switching algebra and the combinational circuit design. Two extended forms of switching functions with the four already existing forms, which will be partly renamed, are presented. Out of combinational circuit design these extended forms, the antivalence of disjunctions A_DF and the equivalence of conjunctions E_cF, are educed and thereby their algebraic expressions are set up. For that, conversion rules which enable the transformation of a disjunction of two variables in equivalence-operation of the same variables and the transformation of a conjunction consisting of two variables in antivalence-operation of the same variables with respect to the extended forms will be lay down. Furthermore, in the case of orthogonal representation of these six function forms relations between them result. That means, by orthogonalization of a corresponding function form it can be easily transformed in an equivalent another function form.