Question

Explain the working of a 4×1 Multiplexer (MUX) with its function table and logic circuit.

Hint:

Number of select lines = \( \log_2(\text{number of inputs}) \). For 4 inputs → \( \log_2 4 = 2 \) select lines.

Answer 1

Concept: A Multiplexer (MUX) is a data selector circuit that:

• Selects one input from multiple inputs.
• Sends the selected input to a single output line.

A 4×1 MUX has:

• 4 data inputs: \( I_0, I_1, I_2, I_3 \)
• 2 select lines: \( S_1, S_0 \)
• 1 output: \( Y \)

Step 1: Working principle.
The select lines determine which input is connected to the output:

• Binary combination of select lines acts as an address.
• Output equals the selected input.

Step 2: Function table.
\[ \begin{array}{|c|c|c|} \hline S_1 & S_0 & Y \\ \hline 0 & 0 & I_0 \\ 0 & 1 & I_1 \\ 1 & 0 & I_2 \\ 1 & 1 & I_3 \\ \hline \end{array} \]
Step 3: Logic expression.
Using sum of products: \[ Y = \overline{S_1}\,\overline{S_0}\,I_0 + \overline{S_1}S_0I_1 + S_1\overline{S_0}I_2 + S_1S_0I_3. \]
Step 4: Logic circuit description.

• Use NOT gates to generate \( \overline{S_1} \) and \( \overline{S_0} \).
• Use four AND gates:
  • AND1: \( \overline{S_1}\overline{S_0}I_0 \)
  • AND2: \( \overline{S_1}S_0I_1 \)
  • AND3: \( S_1\overline{S_0}I_2 \)
  • AND4: \( S_1S_0I_3 \)
• Combine outputs using one OR gate to get \( Y \).

Step 5: Applications.

• Data routing in digital systems
• Communication switching
• CPU data selection
• Parallel-to-serial data conversion

Conclusion:
A 4×1 MUX uses two select lines to choose one of four inputs and route it to a single output using logic gates based on a sum-of-products expression.