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Answer:
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Answer:
Simplification Using Algebraic Functions
In this approach, one Boolean expression is minimized into an equivalent expression by applying Boolean identities.
Problem 1
Minimize the following Boolean expression using Boolean identities −
F(A,B,C)=A′B+BC′+BC+AB′C′
Solution
Given,F(A,B,C)=A′B+BC′+BC+AB′C′
Or,F(A,B,C)=A′B+(BC′+BC′)+BC+AB′C′
[By idempotent law, BC’ = BC’ + BC’]
Or,F(A,B,C)=A′B+(BC′+BC)+(BC′+AB′C′)
Or,F(A,B,C)=A′B+B(C′+C)+C′(B+AB′)
[By distributive laws]
Or,F(A,B,C)=A′B+B.1+C′(B+A)
[ (C' + C) = 1 and absorption law (B + AB')= (B + A)]
Or,F(A,B,C)=A′B+B+C′(B+A)
[ B.1 = B ]
Or,F(A,B,C)=B(A′+1)+C′(B+A)
Or,F(A,B,C)=B.1+C′(B+A)
[ (A' + 1) = 1 ]
Or,F(A,B,C)=B+C′(B+A)
[ As, B.1 = B ]
Or,F(A,B,C)=B+BC′+AC′
Or,F(A,B,C)=B(1+C′)+AC′
Or,F(A,B,C)=B.1+AC′
[As, (1 + C') = 1]
Or,F(A,B,C)=B+AC′
[As, B.1 = B]
So,F(A,B,C)=B+AC′is the minimized form.