Four NOR gates are connected as shown in figure. The truth table for the given figure is :

Four NOR gates are connected as shown in figure. The truth table for the given figure is :

$\begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \hline \end{array}$
$\begin{aligned} &\begin{array}{ccc} A & B & Y \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array} \end{aligned}$
$\begin{aligned} &\begin{array}{ccc}A & B & Y \\ 0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \\1 & 1 & 1 \end{array} \end{aligned}$
$\begin{array}{|c|c|c|}\hline A & B & Y \\\hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\\hline \end{array}$

Solution

$y = \bar{\bar{(A + \bar{A + B})} + \bar{(B + \bar{A + B})}}$

$y = (A + \bar{A + B}) \cdot (B + \bar{A + B})$

$\begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}$

Asked in: JEE Main 2021 (26 Aug Shift 2)

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