A SIMPLE K-MAP BASED VARIABLE SELECTION SCHEME IN THE DIRECT SYNTHESIS OF LOGIC FUNCTIONS WITH MULTIPLEXERS

Abstract

A multiplexer with (n-l) data select inputs can realise directly a function of n variables. In this paper, a simple k-map based variable selection scheme is proposed such that an n variable logic function can be synthesised using a multiplexer with (n-q) data input variables and q data select variables. The procedure is based on the fact that if 2^X minterms (where x = 1, 2, 3) from a minterm list are adjacent on a k-map, the minimised function read from the map contains information on the variable or variables which form the map highest number of l-cubes. 2-cubes or 3-cubes of the function. Such variables have the lowest frequency of occurrence in the minimised function. The criterion for eliminating (n-q) variables from the data select input is to choose (n-q) variables with the lowest frequencies of occurrence in the minimised function and use them as the data input variables of the multiplexer. The data input values of the multiplexer are obtained by constructing a MEV -map using the (n-q) variables as map entered variables and the q data select variables as mapping variables. The procedure is illustrated with examples.