Fast analysis of MUX synthesis of logical functions from the splitting frontiers of the Karnaugh map

A splitting procedure gives 2n regions of equal extent in the Karnaugh map when 2n input MUXs must be used for the synthesis of a logical function. The regions which contain only Os or Is lead to constant data input; the regions containing an equal number of adjacent Os and Is are called ‘typical loops’ and they lead to a variable data input; the remaining regions are split again, and so on. The number of frontiers surrounding the loop of least extent gives the number of levels of the network and the number of the sets of 2n regions gives the number of MUXs used for the synthesis. Examples are presented.