NIMCET 2025 — Computer PYQ
NIMCET | Computer | 2025Consider the Boolean function in a CPU control unit:
Y=(A+B⋅Cˉ)⋅(Aˉ⋅B+C)
Which of the following is the simplified form of Y?
Choose the correct answer:
- A.
A.B+C
- B.
A.C+Aˉ.B+B.Cˉ
- C.
A.C+Aˉ.B.Cˉ
A.C+Aˉ.B.Cˉ
Explanation
To simplify the given Boolean function Y=(A+B.Cˉ).(Aˉ.B+C):
1. Expand the expression:
Y=A.(Aˉ.B)+A.C+B.Cˉ.(Aˉ.B)+B.Cˉ.C
1. Simplify terms using Boolean algebra identities:
• A.Aˉ.B=0.B=0 (since A.Aˉ=0)
• B.Cˉ.Aˉ.B=Aˉ.B.B.Cˉ=Aˉ.B.Cˉ (since B.B=B)
• B.Cˉ.C=B.0=0 (since Cˉ.C=0)
2. Substitute the simplified terms back into the expression:
Y=0+A.C+Aˉ.B.Cˉ+0
1. Final simplified expression:
Y=A.C+Aˉ.B.Cˉ
Comparing this with the given options, the correct answer is (C).
Explanation
To simplify the given Boolean function Y=(A+B.Cˉ).(Aˉ.B+C):
1. Expand the expression:
Y=A.(Aˉ.B)+A.C+B.Cˉ.(Aˉ.B)+B.Cˉ.C
1. Simplify terms using Boolean algebra identities:
• A.Aˉ.B=0.B=0 (since A.Aˉ=0)
• B.Cˉ.Aˉ.B=Aˉ.B.B.Cˉ=Aˉ.B.Cˉ (since B.B=B)
• B.Cˉ.C=B.0=0 (since Cˉ.C=0)
2. Substitute the simplified terms back into the expression:
Y=0+A.C+Aˉ.B.Cˉ+0
1. Final simplified expression:
Y=A.C+Aˉ.B.Cˉ
Comparing this with the given options, the correct answer is (C).