A Comparative Analysis of Multiplexer Techniques for the Minimization of Function Cost Using the Costtable Approach

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 multiplexer, with the goal to find an arrangement of the functions 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 randomly chosen twoand 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.