A comparative analysis of multiplexer techniques for the minimization of function cost using the costtable approach [for costtable read cost-table]

In the cost-table 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. An extension to the cost-table approach in which functions are combined using a multiplexer is shown, with the goal of finding an arrangement of the functions that yields the lowest cost. Specifically, an analysis is made of 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. The relative benefits of (1), (2), and (1) and (2) together are analyzed. The basis of comparison is a set of randomly chosen two- and three-variable four-valued functions. It is shown that these techniques yield a reduction of 7% to 34% in the average cost over the use of a multiplexer without such techniques