228
Digital Electronics
1
1
1
1
1
1
1
1
C
C
B
A
A
D
D
B
Figure 6.21 Solution to example 6.13.
Example 6.14
Minimizing a given Boolean expression using the Quine–McCluskey tabular method yields the following
prime implicants: −0−0, −1−1, 1−10 and 0−00. Draw the corresponding Karnaugh map.
Solution
• As is clear from the prime implicants, the expression has four variables. If the variables are assumed
to be A, B, C and D, then the given prime implicants correspond to the following terms:
1. −0−0 → BBD.
2. −1−1 → BBD.
3. 1−10 → AACCD.
4. 0−00 → AACCD.
• The Karnaugh map can now be drawn as shown in Fig. 6.22.
Example 6.15
AAB + CCD is a simplified Boolean expression of the expression AABBCCD + AABBCCD + AAB. Determine
if there are any ‘don’t care’ entries.
Solution
The expanded version of the given expression is given by the equation
Digital Electronics
1
1
1
1
1
1
1
1
C
C
B
A
A
D
D
B
Figure 6.21 Solution to example 6.13.
Example 6.14
Minimizing a given Boolean expression using the Quine–McCluskey tabular method yields the following
prime implicants: −0−0, −1−1, 1−10 and 0−00. Draw the corresponding Karnaugh map.
Solution
• As is clear from the prime implicants, the expression has four variables. If the variables are assumed
to be A, B, C and D, then the given prime implicants correspond to the following terms:
1. −0−0 → BBD.
2. −1−1 → BBD.
3. 1−10 → AACCD.
4. 0−00 → AACCD.
• The Karnaugh map can now be drawn as shown in Fig. 6.22.
Example 6.15
AAB + CCD is a simplified Boolean expression of the expression AABBCCD + AABBCCD + AAB. Determine
if there are any ‘don’t care’ entries.
Solution
The expanded version of the given expression is given by the equation