ISRO CS 2023 Q.39: solution and answer

ISRO 2023 · CSQ.39 · 1 mark · MCQ

A logic circuit that provides a LOW output when both inputs are HIGH or both inputs are LOW is

See the question in the paper

Answer and solution

ANSWER

The circuit is an XOR gate, option (D).

Take HIGH $= 1$ and LOW $= 0$ . The question gives two rows of the truth table: inputs $00$ give output $0$ , and inputs $11$ give output $0$ . It states nothing about the mixed inputs $01$ and $10$ .
Check each option against both stated rows. AND: $0 \cdot 0 = 0$ but $1 \cdot 1 = 1$ , so the row $11$ fails. NAND: $\overline{0 \cdot 0} = 1$ , so the row $00$ fails. XNOR: $\overline{0 \oplus 0} = 1$ and $\overline{1 \oplus 1} = 1$ , so both rows fail (it gives HIGH when the inputs are equal).
XOR: $Y = A \oplus B = A \overline{B} + \overline{A} B$ . For $00$ : $0 \cdot 1 + 1 \cdot 0 = 0$ . For $11$ : $1 \cdot 0 + 0 \cdot 1 = 0$ . Both stated rows give LOW.
XOR is the only option that gives LOW for both $00$ and $11$ . For the mixed inputs $01$ and $10$ it gives HIGH, so its output is HIGH exactly when the inputs differ.
Hence the gate is XOR.

KEY IDEA

XOR outputs LOW when its two inputs are equal and HIGH when they differ. XNOR is the opposite: HIGH when the inputs are equal.

WATCH OUT FOR

Choosing XNOR because it is the gate that responds to 'both HIGH or both LOW'. XNOR gives HIGH for equal inputs, but the question asks for LOW.