Problem

Solutions For Digital Design Chapter 3 Problem 3P

Step-by-Step Solution

Solution 1

Step #1 of 8

(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.

$C:\Users\vipin.ghildiyal\AppData\Local\Microsoft\Windows\INetCacheContent.Word\721251-3-3P-1.jpg$

Step #2 of 8

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 .

Step #3 of 8

(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.

$C:\Users\vipin.ghildiyal\AppData\Local\Microsoft\Windows\INetCacheContent.Word\721251-3-3P-2.jpg$

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 .

Step #4 of 8

(c)

The Boolean expression is as follows:

The binary equivalent of is as follows:

Step #5 of 8

The K-map representation of the Boolean expression is shown in Figure 3.

$C:\Users\vipin.ghildiyal\AppData\Local\Microsoft\Windows\INetCacheContent.Word\721251-3-3P-3.jpg$

Step #6 of 8

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 .

Step #7 of 8

(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.

$C:\Users\vipin.ghildiyal\AppData\Local\Microsoft\Windows\INetCacheContent.Word\721251-3-3P-4.jpg$

Step #8 of 8

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 .