Automated synthesis of combinational circuits by cascade networks of multiplexers

Knowledge of the advantages of realising VLSI circuits in cellular form have stimulated research in the synthesis of digital circuits by using cellular networks of suitable gates. The cascade network is a special kind of cellular form with a very simple interconnection structure. This paper is concerned with the synthesis of combinational circuits using a cascade of 2-input multiplexer units. A multiplexer unit has been taken as the building block because of its versatility and possibility of use as a universal logic module. Based on the characterising parameters called ´ratio parameters´, an algorithm has been developed to synthesise a given Boolean function by a cascade of two input multiplexers, if realisable. The algorithm is easy to implement on a computer and a program implementing the algorithm in c-language has been developed, thereby allowing automated synthesis. This is essential when the complexity of the digital circuits is high. Both completely specified and incompletely specified functions have been considered.