Boolean Algebra and Simplification Techniques
229
1
1
1
1
1
1
1
1
1
1
CD
AB
A
A
AB
AB
B
B
AB
CD
D
D
CD
CD
Figure 6.22 Solution to example 6.14.
Figure 6.23 Example 6.15.
AABBCCD + AABBCCD + AABBBCCD + CCD + CCD + CCDD
(6.66)
= AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD
D 663
The Karnaugh map for this Boolean expression is shown in Fig. 6.23. Now, if it is to be a simplified
version of the expression AAB + CCD, then the lowermost square in the CD column should not be
empty. This implies that there is a ‘don’t care’ entry. This has been reflected in the map by putting
X in the relevant square. With the groups formed along with the ‘don’t care’ entry, the simplified
expression becomes the one stated in the problem.
229
1
1
1
1
1
1
1
1
1
1
CD
AB
A
A
AB
AB
B
B
AB
CD
D
D
CD
CD
Figure 6.22 Solution to example 6.14.
Figure 6.23 Example 6.15.
AABBCCD + AABBCCD + AABBBCCD + CCD + CCD + CCDD
(6.66)
= AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD + AABBCCD
D 663
The Karnaugh map for this Boolean expression is shown in Fig. 6.23. Now, if it is to be a simplified
version of the expression AAB + CCD, then the lowermost square in the CD column should not be
empty. This implies that there is a ‘don’t care’ entry. This has been reflected in the map by putting
X in the relevant square. With the groups formed along with the ‘don’t care’ entry, the simplified
expression becomes the one stated in the problem.