given a truth table of a logical function, it is possible to write the function as a "product of sums". This is a special form of conjunctive normal form. For example, if given the truth table for the carry-out bit co of one bit position's logic of an adder circuit, as a function of x and y from the addends and the carry in, ci: Observing that the rows that have an output of 0 are the 1st, 2nd, 3rd, and 5th, we can write co as a product of maxterms and . If we wish to verify this: evaluated for all 8 combinations of the three variables will match the table. Dualization The complement of a minterm is the respective maxterm. This can be easily verified by using de Morgan's law. For example: Non-canonical PoS and SoP forms It is often the case that the canonical minterm form can be simplified to an equivalent SoP form. This simplified form would still consist of a sum of product terms. However, in the simplified form, it is possible to have fewer product terms and/or product terms that contain fewer variables. For example, the following 3-variable function: has the canonical minterm representation: , but it has an equivalent simplified form: . In this trivial example, it is obvious that , but the simplified form has both fewer product terms, and the term has fewer variables. The most simplified SoP representation of a function is referred to as a minimal SoP form. In a similar manner, a canonical maxterm form can have a simplified PoS form. While this example was simplified by applying normal algebraic methods [], in less obvious cases a convenient method for finding the minimal PoS/SoP form of a function with up to four variables is using a Karnaugh map. The minimal PoS and SoP forms are important for finding optimal implementations of boolean functions and minimizing logic circuits. Application example The sample truth tables for minterms and maxterms above are sufficient to establish the canonical form for a single bit position in the addition of binary numbers, but are not sufficient to design the digital logic unless your inventory of gates includes AND and OR. Where performance is an issue (as in the Apollo Guidance Computer), the available parts are more likely to be NAND and NOR because of the complementing action inherent in transistor logic. The values are