Adjacency Table Method of Deriving Minimal Sums

Presented in this correspondence is a tabular method for obtaining minimal sum-of-products representations of Boolean functions. The method uses a single table called the adjacency table. This table provides a record of the adjacency properties of the minterms of the given function. In particular, the table records 1) all adjacent pairs of minterms, 2) the variable absent from each product term subsumed by each pair of adjacent minterms, and 3) each minterm that is adjacent to no minterm. From this table, prime implicants of the function are readily determined by using a simple set operation-intersection-on the sets of absent variables.