Evaluate Logic Expression | Boolean Function from The Given Logic Circuit

It is another important topic in the digital electronics course. You are provided with a logic circuit and you have to write its logic expression and truth table. It is also very easy, you just need to practice some questions. 

Example # 1: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[A+B\]	\[(A+B) \oplus \bar A\]
0	0	0	1
0	1	1	0
1	0	1	1
1	1	1	1

Logic Expression: \[(A+B) \oplus \bar A\]

Example # 2: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[C\]	\[A.B\]	\[B+C\]	\[(A.B).(B+C)\]
0	0	0	0	0	0
0	0	1	0	1	0
0	1	0	0	1	0
0	1	1	0	1	0
1	0	0	0	0	0
1	0	1	0	1	0
1	1	0	1	1	1
1	1	1	1	1	1

Logic Expression: \[(A.B).(B+C)\]

Example # 3: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[\overline {A+B}\]	\[\overline {A.B}\]	\[\overline {A+B} \oplus \overline {A.B}\]
0	0	1	1	0
0	1	0	0	0
1	0	0	0	0
1	1	0	0	0

Logic Expression: \[\overline {A+B} \oplus \overline {A.B}\]

Example # 4: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[A.B\]	\[\overline {A.B}\]	\[\overline {(A.B) \oplus (\overline{A.B})}\]
0	0	0	1	0
0	1	0	1	0
1	0	0	1	0
1	1	1	0	0

Logic Expression: \[\overline {(A.B) \oplus (\overline{A.B})} \]

Example # 5: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[A.B\]	\[\bar A.B\]	\[(A.B)+(\bar A.B)\]
0	0	0	0	0
0	1	0	1	1
1	0	0	0	0
1	1	1	0	1

Logic Expression: \[(A.B)+(\bar A.B)\]

Example # 6: A logic circuit is given, evaluate its Boolean/ logic expression and truth table:

\[A\]	\[B\]	\[C\]	\[A+B\]	\[\bar A+\bar C\]	\[(A+B)+(\bar A+\bar C)\]
0	0	0	0	1	1
0	0	1	0	1	1
0	1	0	1	1	1
0	1	1	1	1	1
1	0	0	1	1	1
1	0	1	1	0	1
1	1	0	1	1	1
1	1	1	1	0	1

Logic Expression: \[(A+B)+(\bar A+\bar C)\]

Example # 7: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[C\]	\[A+B\]	\[\bar A.\bar B\]	\[\overline {\bar B \oplus C}\]	\[\overline {(A+B).(\bar A.\bar B)}\]	\[\overline {\overline {(A+B).(\bar A.\bar B)} + \overline {(\bar B \oplus C)}}\]
0	0	0	0	1	0	1	0
0	0	1	0	1	1	1	0
0	1	0	1	0	1	1	0
0	1	1	1	0	0	1	0
1	0	0	1	0	0	1	0
1	0	1	1	0	1	1	0
1	1	0	1	0	1	1	0
1	1	1	1	0	0	1	0

Logic Expression: \[\overline {\overline {(A+B).(\bar A.\bar B)} + \overline {(\bar B \oplus C)}}\]

Example # 8: A logic circuit is given, evaluate its truth table :

\[A\]	\[B\]	\[C\]	\[D\]	\[A+\bar B\]	\[\bar A+ B\]	\[C.D\]	\[\overline {(A+\bar B) \oplus (\bar A+B)}\]	\[\overline {\overline {(A+\bar B) \oplus (\bar A+B)} \oplus (C.D)}\]
0	0	0	0	1	1	0	1	0
0	0	0	1	1	1	0	1	0
0	0	1	0	1	1	0	1	0
0	0	1	1	1	1	1	1	1
0	1	0	0	0	1	0	0	1
0	1	0	1	0	1	0	0	1
0	1	1	0	0	1	0	0	1
0	1	1	1	0	1	1	0	0
1	0	0	0	1	0	0	0	1
1	0	0	1	1	0	0	0	1
1	0	1	0	1	0	0	0	1
1	0	1	1	1	0	1	0	0
1	1	0	0	1	1	0	1	0
1	1	0	1	1	1	0	1	0
1	1	1	0	1	1	0	1	0
1	1	1	1	1	1	1	1	1

Logic Expression: \[\overline {\overline {(A+\bar B) \oplus (\bar A+B)} \oplus (C.D)}\]

Example # 9: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[C\]	\[A.B\]	\[B.C\]	\[(A.B)+(B.C)\]
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

Logic Expression: \[(A.B)+(B.C)\]

Example # 10: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[\overline {A+B}\]	\[A.\bar B\]	\[\overline {(\bar A+B).(A.\bar B)}\]
0	0	1	0	1
0	1	0	0	1
1	0	0	1	1
1	1	0	0	1

Logic Expression: \[\overline {(\bar A+B).(A.\bar B)}\]

Example # 11: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[C\]	\[D\]	\[\overline {A.B}\]	\[\overline {B+C}\]	\[\overline {C\oplus D}\]	\[\overline {A.B}).(\overline {B+C})\]	\[(\overline {A.B}).(\overline {B+C})+ (\overline {C\oplus D})\]
0	0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1	1
0	0	1	0	1	0	0	0	0
0	0	1	1	1	0	1	0	1
0	1	0	0	1	0	1	0	1
0	1	0	1	1	0	0	0	0
0	1	1	0	1	0	0	0	0
0	1	1	1	1	0	1	0	1
1	0	0	0	1	1	1	1	1
1	0	0	1	1	1	0	1	1
1	0	1	0	1	0	0	0	0
1	0	1	1	1	0	1	0	1
1	1	0	0	0	0	1	0	1
1	1	0	1	0	0	0	0	0
1	1	1	0	0	0	0	0	0
1	1	1	1	0	0	1	0	1

Logic Expression: \[(\overline {A.B}).(\overline {B+C})+ (\overline {C\oplus D})\]

Example # 12: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[C\]	\[\bar A+\bar B\]	\[\overline {B\oplus C}\]	\[(\bar A+\bar B).(\overline {B\oplus C})\]
0	0	0	1	1	1
0	0	1	1	0	0
0	1	0	1	0	0
0	1	1	1	1	1
1	0	0	1	1	1
1	0	1	1	0	0
1	1	0	0	0	0
1	1	1	0	1	0

Logic Expression: \[(\bar A+\bar B).(\overline {B\oplus C})\]

Example # 13: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[C\]	\[\bar A \oplus B\]	\[\overline {A \oplus B}\]	\[B+C\]	\[(\bar A \oplus B).\\(\overline {A \oplus B})\]	\[(\bar A\oplus B).\\(\overline {A \oplus B}).(B+C)\]
0	0	0	1	1	0	1	0
0	0	1	1	1	1	1	1
0	1	0	0	0	1	0	0
0	1	1	0	0	1	0	0
1	0	0	0	0	0	0	0
1	0	1	0	0	1	0	0
1	1	0	1	1	1	1	1
1	1	1	1	1	1	1	1

Logic Expression: \[(\bar A\oplus B).(\overline {A \oplus B}).(B+C)\]

Example # 14: A logic circuit is given, evaluate its Boolean/ logic expression:

\[A\]	\[B\]	\[\bar A.\bar B\]	\[\bar A+\bar B\]	\[(\overline {\bar A.\bar B)\oplus (\bar A+\bar B)}\]
0	0	1	1	1
0	1	0	1	0
1	0	0	1	0
1	1	0	0	1

Logic Expression: \[\overline {(\bar A.\bar B)\oplus (\bar A+\bar B)}\]

Example # 15: A logic circuit is given, evaluate its Boolean/ logic expression

\[A\]	\[B\]	\[\overline {A+B}\]	\[\overline {A.B}\]	\[(\overline {A+B}). (\overline {A.B})\]
0	0	1	1	1
0	1	0	1	0
1	0	0	1	0
1	1	0	0	0

Logic Expression: \[(\overline {A+B}).(\overline {A.B})\]

Example # 16: A logic circuit is given, evaluate its Boolean/ logic expression

\[A\]	\[B\]	\[C\]	\[A.C\]	\[C.B\]	\[\overline {(A.C).(C.B)}\]
0	0	0	0	0	1
0	0	1	0	0	1
0	1	0	0	0	1
0	1	1	0	1	1
1	0	0	0	0	1
1	0	1	1	0	1
1	1	0	0	0	1
1	1	1	1	1	0

Logic Expression: \[\overline {(A.C).(C.B)}\]

Example # 17: A logic circuit is given, evaluate its Boolean/ logic expression

\[A\]	\[B\]	\[C\]	\[A+C\]	\[\bar A+B\]	\[(A+C) \oplus (\bar A+B)\]
0	0	0	0	1	1
0	0	1	1	1	0
0	1	0	0	1	1
0	1	1	1	1	0
1	0	0	1	0	1
1	0	1	1	0	1
1	1	0	1	1	0
1	1	1	1	1	0

Logic Expression: \[(A+C) \oplus (\bar A+B)\]

Example # 18: A logic circuit is given, evaluate its Boolean/ logic expression

\[A\]	\[B\]	\[C\]	\[D\]	\[A.\bar B\]	\[\overline {A.B}\]	\[(A.\bar B) \\ \oplus \overline {(A.B)}\]	\[B+\bar C\]	\[\overline {C+D}\]	\[(A.\bar B) \oplus \overline {(A.B)}\\+ (B+\bar C)\]	\[(A.\bar B) \oplus \overline {(A.B)} + \\(B+\bar C) \oplus \overline {(C+D)}\]
0	0	0	0	0	1	1	1	1	1	0
0	0	0	1	0	1	1	1	0	1	1
0	0	1	0	0	1	1	0	0	1	1
0	0	1	1	0	1	1	0	0	1	1
0	1	0	0	0	1	1	1	1	1	0
0	1	0	1	0	1	1	1	0	1	1
0	1	1	0	0	1	1	1	0	1	1
0	1	1	1	0	1	1	1	0	1	1
1	0	0	0	1	1	0	1	1	1	0
1	0	0	1	1	1	0	1	0	1	1
1	0	1	0	1	1	0	0	0	0	0
1	0	1	1	1	1	0	0	0	0	0
1	1	0	0	0	0	0	1	1	1	0
1	1	0	1	0	0	0	1	0	1	1
1	1	1	0	0	0	0	1	0	1	1
1	1	1	1	0	0	0	1	0	1	1

Logic Expression: \[(A.\bar B) \oplus \overline {(A.B)}  + (B+\bar C) \oplus \overline {(C+D)}\]