Q 12-14-157JEE MainJEE Main 2021 (26 Aug, Shift 2)Medium
Four NOR gates are connected as shown in figure. The truth table for the given figure is:
Answer: (C) $\begin{array}{cc|c} A & B & Y \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \end{array}$
Let $C = \overline{A + B}$ be the output of the first NOR gate. The second and third gates give $\overline{A + C}$ and $\overline{B + C}$, and the last gate gives
$$Y = \overline{\overline{A + C} + \overline{B + C}} = (A + C)(B + C) = AB + C = AB + \bar{A}\bar{B}$$
This is XNOR: $Y = 1$ for $(0,0)$ and $(1,1)$, and $Y = 0$ for $(0,1)$ and $(1,0)$.
Solution by Sreeraj P, M.Sc Physics