216
Digital Electronics
The 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
2
0
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
ABC
000
010
011
101
110
111
010
011
100
110
111
0−0
1−0
1−1
−1−
From the prime implicant table, the minimized output Boolean functions can be written as follows:
Y 1 = B + AAC + AAC
(6.42)
Y 2 = B + AAC
(6.43)
6.6 Karnaugh Map Method
A Karnaugh map is a graphical representation of the logic system. It can be drawn directly from either
minterm (sum-of-products) or maxterm (product-of-sums) Boolean expressions. Drawing a Karnaugh
map from the truth table involves an additional step of writing the minterm or maxterm expression
depending upon whether it is desired to have a minimized sum-of-products or a minimized productof-sums expression.
6.6.1 Construction of a Karnaugh Map
An n-variable Karnaugh map has 2
n squares, and each possible input is allotted a square. In the case
of a minterm Karnaugh map, ‘1’ is placed in all those squares for which the output is ‘1’, and ‘0’