is true only when a and c both are true and b is false—the input arrangement where a = 1, b = 0, c = 1 results in 1. Given the truth table of a logical function, it is possible to write the function as a "sum of products". This is a special form of disjunctive normal form. For example, if given the truth table for the arithmetic sum bit u 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 1 are the 2nd, 3rd, 5th, and 8th, we can write u as a sum of minterms and . If we wish to verify this: evaluated for all 8 combinations of the three variables will match the table. Maxterms For a boolean function of variables , a sum term in which each of the variables appears once (either in its complemented or uncomplemented form) is called a maxterm. Thus, a maxterm is a logical expression of variables that employs only the complement operator and the disjunction operator. Maxterms are a dual of the minterm idea (i.e., exhibiting a complementary symmetry in all respects). Instead of using ANDs and complements, we use ORs and complements and proceed similarly. For example, the following are two of the eight maxterms of three variables: a + b′ + c a′ + b + c There are again 2n maxterms of variables, since a variable in the maxterm expression can also be in either its direct or its complemented form—two choices per variable. Indexing maxterms Each maxterm is assigned an index based on the opposite conventional binary encoding used for minterms. The maxterm convention assigns the value 0 to the direct form and 1 to the complemented form . For example, we assign the index 6 to the maxterm (110) and denote that maxterm as M6. Similarly M0 of these three variables is (000) and M7 is (111). Functional equivalence It is apparent that maxterm n gives a false value (i.e., 0) for just one combination of the input variables. For example, maxterm 5, a′ + b + c′, is false only when a and c both are true and b is false—the input arrangement where a = 1, b = 0, c = 1 results in 0. If one is