Representations of logic functions

Logic function representations play an important role in logic design and computer design, as well as VLSI design. There are many ways to represent a logic function. Presents and classifies 11 representation methods into “unique representation category” and “non‐unique representation category”. History of these methods is also briefly mentioned. There are three non‐unique representation methods: Boolean expression;sum of products; and product sums, and eight unique representation methods: truth table; canonical sum of products; canonical product of sums; sum of minterms; product of maxterms; Karnaugh map; Boolean lattice; and Venn diagram. A theorem is found which states that Boolean expression, sum of products, product of sums, sum of minterms, product of maxterms, and Karnaugh map, form a lattice structure. The results may have useful applications in knowledge representation, pictorial knowledge representation and other related areas.