Multi-output, multi-level, multi-gate design using non-linear programming

Abstract: Using logic gates is the traditional way of designing logic circuits. However, most of the minimization algorithms concern a limited set of gates (complete sets), like sum of products, exclusive-or sum of products, NAND gates, NOR gates e.t.c.. In this paper, a method is proposed for minimizing multi-output Boolean functions using any kind of two-input gates although it can easily be extended to multi-input gates. The method is based on non-linear mixed integer programming. The experimental results show that the method gives the same or better results compared to other methods available in the literature. However, other methods do not ensure that they produce the minimal solution, while the main advantages of the proposed method are that it does guarantee minimality and it can also handle Boolean functions for incompletely specified functions. The method is general enough and can easily be extended to more complicated design modules than just basic gates.