A Comparative analysis of multiplexer techniques for the minimization of function cost using the cost-table approach

Abstract

In the costtable approach to logic design, a given function is realized by selecting functions from a table and combining them. Associated with each function is a cost, and the goal is to find, among all realizations, the one of least cost. We show an extension to the costtable approach in which functions are combined using a multi- plexer, with the goal to find an arrangement of the func- tions that yields the lowest cost. Specifically, we analyze two techniques to minimize total function cost 1) choosing which variables to apply to the multiplexer inputs and 2) choosing a permutation of logic values that yields lowest cost. We analyze the relative benefits of l), 2), and 1) and 2) together. Our basis of comparison is a set of ran- domly chosen two- and three-variable 4-valued functions. We show that these techniques yield a reduction of 7 to 34% in the average cost over the use of a multiplexer without such techniques.