Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 5 M

Year: Dec 2014

$$\overline{\overline{AB+\overline{A}\overline{B}}+\overline{{(A+B)}(\overline{A}+B)}}$$

$\overline{\overline{AB\bullet\overline{AB}}+\overline{A+B}+\overline{(\overline{A}+B})}.................\text{DeMorgan's Theorems}$

$\overline{\overline{AB}}+\overline{A+B}\bullet\overline{\overline{A+B}}\bullet\overline{\overline{\overline{A}+B}}.................\text{DeMorgan's Theorems}$

$AB+\overline{A+B}\bullet(A+B)\bullet(\overline{A}+B)$

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$AB+\overline{AB}[A\overline{A}+AB+\overline{A}B+BB]..............\text{Simplification}$

$AB+\overline{AB}[0+AB+\overline{A}B+B]................As \ A\overline{A}=0 \ \ \& BB=B$

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$AB+\overline{A}\overline{B}[B(A+\overline{A}+1)]...............A+\overline{A}+1=1$

$AB+\overline{A}\overline{B}(B)$

$AB+\overline{A}\overline{B}B \hspace{0.9cm}As \ \overline{B}B=0$

$AB$

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Implementation using AOI Gate.