Two Level Logic Minimization: Given a switching function with on-set F = {f*}, d

Question

Two Level Logic Minimization: Given a switching function with on-set F = {f*}, don't-care set D = {di} and off-set R{ri}, where each fi, di, or ri is a product term. In addition we have all the prime implicants P = {pi}. We want to identify the essential prime implicants for a two level logic minimization. State the definition of the essential prime implicant. Suppose that you are the chief software engineer. We need a high level pseudo code to identify that prime implicant pi is essential. Write the pseudo code and explain your algorithm. Hint: Assume that you have some low level routines available for the pseudo code. Some (not all) possible routines are listed below. You may define and use similar routines in your algorithm. adjacency (pi, pj): returns true if product terms pi and pj are adjacent, otherwise returns false. consensus(pi, pj): returns the consensus if the two product terms p, and pj are adjacent, otherwise returns an empty set. tautology(S): The set S contains a list of product terms. This routine returns true if the sum of all product terms in the set S is always true for any input combination, otherwise it returns false.

Explanation / Answer

A prime implicant of a function is an implicant that cannot be covered by a more general (more reduced - meaning with fewer literals) implicant. W.V. Quine defined a prime implicant of F to be an implicant that is minimal - that is, the removal of any literal from P results in a non-implicant for F. Essential prime implicants are prime implicants that cover an output of the function that no combination of other prime implicants is able to cover.

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http://webdocs.cs.ualberta.ca/~amaral/courses/329/webslides/Topic4-KarnaughMaps/sld001.htm

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