BOOLEAN FUNCTION “EXCLUSIVE OR” FOR THE N VARIABLES

Abstract

This paper proposes a new Boolean function – "exclusive OR" for case of n Boolean variables. The definition of this function is given; its basic properties are studied. In particular, it is established (theorem) that the "exclusive OR" of n variable is a symmetric function with respect to the permutation of arguments, and in the case n = 2 coincides with the "exclusive OR". For the cases n = 3;4, a disjunctive normal form (DNF), perfect disjunctive normal form (PDNF), minimal disjunctive normal form are constructed. In particular, in the case of n = 3, three equal minimal disjunctive normal forms were found using the Quine method. It is established that the conjunctive normal form, the perfect conjunctive normal form and the minimized conjunctive normal form coincide with the definition of the "exclusive OR" of n variable. For the cases n = 3;4, Zhegalkin polynomials are constructed, which are of the order of one lower than PDNF. Post classification performed. It is established that the "exclusive OR" for the cases of n = 3.4 belongs to the class, does not belong to the classes  and , is not a monotonic and self- double function.