КОНЦЕПЦІЯ ОПТИМАЛЬНОЇ ФОРМИ ПРЕДСТАВЛЕННЯ ЛОГІЧНИХ ФУНКЦІЙ ТА ПРОБЛЕМИ ЇЇ ВПРОВАДЖЕННЯ

Abstract

In scientific publications and conducted studies, the possibility of representing logical functions (LF) in alternative forms of representation is demonstrated, the characteristic feature of which is a polynomial entity, which reduces to the representation of LF in the form of series different from the traditional classical representation by adding members of a series - in particular, for an algebraic form, the addition is carried out algebraically with weight coefficients, and in the case of the use of the Reed-Muller form addition is made for mod 2. The results of complete sets of logical functions studies proved that the traditional classical form does not always ensure the minimality of indicators for the structural complexity of the logical functions implementation, which makes relevant further steps in determining the optimal forms for representing logical functions in the problems of discrete devices analysis and synthesis. The implementation of the combination scheme for a given logical function from n arguments is carried out by some set of variants of structures. In problems of analysis and synthesis of combinational circuits of discrete devices it is necessary to evaluate the quality of their possible structures, to provide identification and selection of the most successful or optimal ones. The concept of the logical functions optimal form of representation is presented in the article as an important direction of structural perfection of discrete devices on the basis of their logical functions realization in alternative forms of representation. The existence of the OFR-concept, which takes into account different forms of representation, makes it highly efficient to use alternative forms of logical functions representation from the point of the structural complexity parameters of the combinational schemes implementation in comparison with traditional classical form. The article outlines the factors for the further improvement of the OFR-concept by filling it with new scientific achievements, which will allow to completely or partially remove difficulties with the introduction of the optimal FR into broad engineering practice