Realization of Arbitrary Logical Functions Using Majority Elements

A method is developed for the synthesis of arbitrary combinational logical functions using three-input majority elements. The networks that result are in the form of modified trees. It is shown that an average saving of 30 per cent in majority elements is made on trees of majority elements which individually produce ``AND'' and ``OR'' functions. Several variations of the basic method are developed and the results are compared with the algebraic methods of Cohn and Lindaman.