Majority Gate Networks

Some new procedures for synthetizing three-input majority gate networks have been described. Both a geometrical approach on the map of the assigned function and an algebraic procedure have been discussed. The geometrical methods give a number of different solutions and may lead to the simplest networks, but their use requires ingenuity. Therefore, some of the solutions suggested by the analysis of the maps have been translated into algebraic expressions, which may be easily used for automatic computation. The techniques described are applicable to any and all Boolean functions and lead to simple solutions. In fact, every function of n variables can be implemented by a network having (n-1) levels of gates, if n is odd, or n levels, if n is even, at the most. All the procedures are relatively simple and can be extended to the synthesis of networks of any type (m, t).