Question

Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for $A_0, A_1, A_2,$ and $A_3$ are ________________.

• A. $A_0 = 0,\; A_1 = 0,\; A_2 = 1,\; A_3 = 1$
• B. $A_0 = 1,\; A_1 = 0,\; A_2 = 1,\; A_3 = 0$
• C. $A_0 = 0,\; A_1 = 1,\; A_2 = 1,\; A_3 = 0$
• D. $A_0 = 1,\; A_1 = 1,\; A_2 = 0,\; A_3 = 0$

Hint:

To implement a logic function using a MUX, map the function output values directly to the MUX inputs according to the select-line combinations.

Answer 1

The Correct Option is C

A 4-to-1 MUX outputs one of the four inputs $A_0, A_1, A_2, A_3$ based on the select lines \[ S_1 = C,\qquad S_0 = D. \]
We want the output to be: \[ \text{OUTPUT} = C \oplus D. \]
Step 1: Write the truth table for XOR. \[ \begin{array}{c c | c} C & D & C \oplus D \\ \hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{array} \]
Step 2: Match select inputs to MUX inputs.
The MUX mapping is: \[ S_1 S_0 = CD: \] \[ 00 \rightarrow A_0,\quad 01 \rightarrow A_1,\quad 10 \rightarrow A_2,\quad 11 \rightarrow A_3. \]
Thus, to generate XOR: \[ A_0 = 0,\quad A_1 = 1,\quad A_2 = 1,\quad A_3 = 0. \]
These values match option (C).
Final Answer: $A_0 = 0,\; A_1 = 1,\; A_2 = 1,\; A_3 = 0$