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Prove the following identities a. A‾B‾C‾ + A‾BC‾ + AB‾C‾ + ABC‾ = C‾ b. AB + ABC + A‾ B + AB‾C = B + AC
Ans.
a. LHS = A'B'C' + A'BC' + AB'C' + ABC'= A'C' (B' + B) + AC' (B' + B)= A'C' + AC' [as B'+B = 1]= C' (A' + A)= C' [since A'+A =1]= RHS.Thus Provedb. LHS = AB + ABC + A'B + AB'C
= B + AC= B (A + A') + AC (B + B')= B + AC [as B + B' = A + A' = 1]= B + AC= RHS.Thus Proved
The logic circuit shown in the given figure can be minimised to Ans. The minimised figure of logic diagram is D, the output of the logic circuit is as Y=(X+Y')'+(X'+(X+
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