JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Semiconductors

The expression $Y=A\bar{B}C+\bar{A}\bar{C}$ is a sum of two product terms. The first term $A\bar{B}C$ requires $B$ inverted and then a three-input AND of $A,\bar{B},C$. The second term $\bar{A}\bar{C}$ can be built either by inverting $A$ and $C$ and taking a two-input AND, or by recognising that $\bar{A}\bar{C}=\overline{A+C}$, which a single two-input NOR gate gives directly. The two terms are then combined in a two-input OR gate. The arrangement using a three-input AND, three NOT gates, a two-input AND and an OR gate reproduces $Y$, and so does the one using a three-input AND, one NOT gate, a two-input NOR and an OR gate; an arrangement built around a three-input OR gate cannot. Only those first two gate arrangements realise $Y$.