Digital Electronics: Principles, Devices and Applications

216 Digital ElectronicsThe different steps leading to construction of the prime implicant table are given in tabular form below:A B C 1 2 A B C 1 2 A B C 1 20 0 0 ̌ ̌ 0 − 0 ̌ * − 1 − ̌ ̌ *0 1 0 ̌ ̌ ̌ 0 1 − ̌ ̌ ̌1 0 0 ̌ ̌ − 1 0 ̌ ̌ ̌1 − 0 ̌ *0 1 1 ̌ ̌ ̌1 0 1 ̌ ̌ − 1 1 ̌ ̌ ̌1 1 0 ̌ ̌ ̌ 1 − 1 ̌ *1 1 − ̌ ̌ ̌1 1 1 ̌ ̌ ̌Y 1 Y 2 ABC000 010 011 101 110 111 010 011 100 110 111̌ ̌ 0−0̌ ̌ 1−0̌ ̌ 1−1̌ ̌ ̌ ̌ ̌ ̌ ̌ ̌ −1−From the prime implicant table, the minimized output Boolean functions can be written as follows:Y 1 = B + AC + AC (6.42)Y 2 = B + AC (6.43)6.6 Karnaugh Map MethodA Karnaugh map is a graphical representation of the logic system. It can be drawn directly from eitherminterm (sum-of-products) or maxterm (product-of-sums) Boolean expressions. Drawing a Karnaughmap from the truth table involves an additional step of writing the minterm or maxterm expressiondepending upon whether it is desired to have a minimized sum-of-products or a minimized productof-sumsexpression.6.6.1 Construction of a Karnaugh MapAn n-variable Karnaugh map has 2 n squares, and each possible input is allotted a square. In the caseof a minterm Karnaugh map, ‘1’ is placed in all those squares for which the output is ‘1’, and ‘0’