Question

In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

• A. $Y=PQ$
• B. $Y=P+Q$
• C. $Y=\overline{P}\,Q$
• D. $Y=\overline{P}+\overline{Q}$

Hint:

Always reduce a $2\times1$ MUX to $Y=\overline{S}I_0+SI_1$ and then plug in the connected signals.

Answer 1

The Correct Option is A

Step 1: Interpret the $2\times1$ MUX connections.
From the figure: $I_0$ is tied to $0$ (ground), $I_1$ is $P$, and the select input is $Q$. 
Step 2: Write the MUX output equation.
For a $2\times1$ MUX, \[ Y=\overline{Q}\,I_0+Q\,I_1. \] Substitute $I_0=0$ and $I_1=P$: \[ Y=\overline{Q}. 0+Q. P=PQ. \] \[ \boxed{Y=PQ} \]