Question 2016.S2.26: The Boolean expression (a +b +c +d)+(b + c ) simplifies to (......

Wiley Acing The Gate Electrical Engineering [1079382]

The Boolean expression $\overline{(a+\bar{b}+c+\bar{d})+(b+\bar{c})}$ simplifies to

(a) 1 (b) $\overline{a, b}$

(c) a, b (d) 0

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The given function

$F=\overline{(a+\bar{b}+c+\bar{d})+(b+\bar{c})}$

can be simplified using De Morgan’s theorem as

$\begin{aligned}F & =(\overline{a+\bar{b}+c+\bar{d}}) \cdot(\overline{b+\bar{c}}) \\& =(\bar{a} \cdot b \cdot \bar{c} \cdot d) \cdot(\bar{b} c) \\& =0\end{aligned}$

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