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The De Morgan dual is the canonical conjunctive normal form , maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.
In sum-of-products (SOP) form, AND gates form the smallest unit and are stitched together using ORs, whereas in product-of-sums (POS) form it is opposite. POS form requires parentheses to group the OR terms together under AND gates, because OR has lower precedence than AND. Both SOP and POS forms translate nicely into circuit logic.
A sum-of-products expression (SOP) can always be implemented using AND gates feeding into an OR gate, and a product-of-sums expression (POS) leads to OR gates feeding an AND gate. The POS expression gives a complement of the function (if F is the function so its complement will be F'). [10]
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.
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This expression says that the output function f will be 1 for the minterms ,,,, and (denoted by the 'm' term) and that we don't care about the output for and combinations (denoted by the 'd' term). The summation symbol ∑ {\displaystyle \sum } denotes the logical sum (logical OR, or disjunction) of all the terms being summed over.
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