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Boolean Expression To Logic Circuit Solved Examples
Boolean Expression/Function to Logic Circuit and Truth Table Evaluation
This topic is important from the examination point of view. It is easy and you can do it in a couple of minutes. You are given an expression and you have to draw a logic circuit for this expression. I will explain with the help of examples. Some points to follow,
Look for parentheses, draw them first
Proceed from left to right
There are no other rules or suggestions for solving these exercises. Just do some examples.
Example # 1: \[(A+B).A\]
A
B
Output
0
0
0
0
1
0
1
0
1
1
1
1
Example # 2: \[(\bar A+B).B\]
A
B
Output
0
0
1
0
1
1
1
0
0
1
1
0
Example # 3: \[(\bar A. \bar B)+ B\]
A
B
Output
0
0
1
0
1
1
1
0
0
1
1
1
Example # 4: \[(A.B) \oplus C\]
A
B
C
\[A.B\]
\[(A.B) \oplus C\]
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
Example # 5: \[A.B + B.C\]
A
B
C
\[A.B\]
\[B.C\]
\[A.B + B.C\]
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
Example # 6: \[(A+B).(A+C)\]
A
B
C
\[A+B\]
\[A+C\]
\[(A+B).(A+C)\]
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
Example # 7: \[(\bar A \oplus B).(A \oplus C)\]
A
B
C
\[\bar A \oplus B\]
\[A \oplus C\]
\[(\bar A \oplus B).(A \oplus C)\]
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
Example # 8: \[A . B + A . C \oplus C . D\]
A
B
C
D
\[A.B\]
\[A.C\]
\[C.D\]
\[A.B+A.C\]
\[A . B + A . C \oplus C . D\]
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
Example # 9: \[(A + B) \oplus (A . C)\]
A
B
C
\[A+B\]
\[A.C\]
\[(\bar A \oplus B).(A \oplus C)\]
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
Example # 10: \[A . B + B . C + (C \oplus D)\]
A
B
C
D
\[A.B\]
\[B.C\]
\[C \oplus D\]
\[A.B + B.C\]
\[A . B + B . C + (C \oplus D)\]
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
Example # 11: \[(\bar A . \bar B) \oplus (A + \bar B)\]
A
B
\[\bar A. \bar B\]
\[A + \bar B\]
\[(\bar A . \bar B) \oplus (A + \bar B)\]
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
Example # 12: \[(\bar A . B) + \bar C\]
A
B
C
\[\bar A.B\]
\[(\bar A . B) + \bar C\]
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
Example # 13: \[\overline {(\bar A +\bar B) \oplus (B+C)}\]
A
B
C
\[\bar A + \bar B\]
\[B+C\]
\[\overline {(\bar A+\bar B) \oplus (B+C)}\]
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
Example # 14: \[\overline {A.B} + \overline{C+B}\]
A
B
C
\[\overline {A.B}\]
\[\overline {C+B}\]
\[\overline {A.B} + \overline{C+B}\]
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
Example # 15: \[\overline {(A.\bar C) +(\overline{C.B})}\]
A
B
C
\[A. \bar C\]
\[\overline {C.B}\]
\[\overline {(A.\bar C) +(\overline{C.B})}\]
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
Example # 16: \[\overline {(\overline {B+C}).(\overline {B.C})}\]
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