Page 89 - Computer science 868 Class 12
P. 89
Ans. A' (A+B')'-A"+B"-A+B
B'
(A'+C)'
-A"+C' ((A+B).(A+C).(A'+C'))'
A' -A+C' (A+B).(A+C).(A'+C')'
C
A' (A'+C)'
(AC)'
C'
-A'+C'
9. Write the boolean expression of (1), (2), (3) and (4) for the following logic circuit diagram and finally minimise the given
expression.
A (1)
B (2)
C
(4)
A (3)
B
Ans. 1. (A.B.C)' 2. (A.B.C)'+C 3. (A+B)' 4. ((A.B.C)'+C).(A+B)'
Simplify the final result
((A.B.C)'+C).(A+B)'
= (A'+B'+C'+C).A'.B' [ (X.Y)'=X'+Y' (X+Y)'=X'.Y']
= (A'+B'+ 1).A'.B' [ X+X'=1]
= 1.A'.B' [ X+1=1]
= A'.B' [X.1=X]
10. Write the boolean expression of (1), (2), (3) and (4) for the following logic circuit diagram and finally minimise the given
expression.
A (1)
B
C
A' (2) (4)
B
C
A (3)
B
C'
Ans. 1. (A.B.C)' 2. (A'.B.C)' 3. (A.B.C')' 4. (A.B.C)'+(A'.B.C)'+(A.B.C')'
Simplification
(A.B.C)'+(A'.B.C)'+(A.B.C')'
= A'+B'+C'+A"+B'+C'+A'+B'+C" [DeMorgan’s Law]
= A'+B'+C'+A+B'+C'+A'+B'+C [Involution law]
= (A+A')+(C+C')+B'+C' [Associative law & Idempotent law]
= 1+B'+C' [Complement law]
= 1 [Properties of 0 and 1]
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Computer Hardware 87

