Canonical and Standard forms

A binary variable may be either in its true form or its complement . For n variables, the maximum number of input variable combinations is given by N = 2 ⁿ. Then considering the AND gate, each of the N logic expressions formed is called a standard product or minterm. As indicated in Table 1-13, binary digits '1' and '0' are taken to represent a given variable for example or its complement respectively. Also from Table 1-13 note that each minterm is assigned a symbol (P _j) each where j is the decimal equivalent to the binary number of the minterm designated.

Similarly, if we consider an OR gate, each of the N logic expressions formed is called a standard sum or maxterm. In this case binary digits '1' and '0' are taken to represent a given complemented variable and its true form respectively. As shown in Table 1-13, a symbol (S _j) is assigned to each maxterm where j is the decimal equivalent to the binary number of the maxterm designated. Also observe that each maxterm is the complement of its corresponding minterm, and vice versa.