(a)
The Boolean expression is as follows:
The binary equivalent of is as follows:
The K-map representation of the Boolean expression is shown in Figure 1.
In the K-map shown in Figure 1, there are 2 distinct combinations that are formed: the first, represented by the yellow color is a pair (combination of 2 squares) with value ; and the second, represented by the brown color is a pair with value .
The simplified Boolean function is the sum of the individual terms obtained.
Hence, the simplified Boolean expression is .
(b)
The Boolean expression is as follows:
The binary equivalent of is as follows:
The K-map representation of the Boolean expression is shown in Figure 2.
In the K-map shown in Figure 2, there are 2 distinct combinations that are formed: the first, represented by the blue color is a quad (combination of 4 squares) with value ; the second, represented by the brown color is a pair (combination of 2 squares) with value .
The simplified Boolean function is the sum of the individual terms obtained.
Hence, the simplified Boolean expression is .
(c)
The Boolean expression is as follows:
The binary equivalent of is as follows:
In the K-map shown in Figure 3, there are 2 distinct combinations that are formed: the first, represented by the brown color is a quad (combination of 4 squares) with value ; the second, represented by the blue color is a pair (combination of 2 squares) with value .
The simplified Boolean function is the sum of the individual terms obtained.
Hence, the simplified Boolean expression is .
(d)
The Boolean expression is as follows:
The binary equivalent of is as follows:
The K-map representation of the Boolean expression is shown in Figure 4.
In the K-map shown in Figure 3, there are 2 distinct combinations that are formed: the first, represented by the green color is a pair (combination of 2 squares) with value ; the second, represented by the blue color is the minterm (only one square) with value .
The simplified Boolean function is the sum of the individual terms obtained.
Hence, the simplified Boolean expression is .