Multiplexer (MUX) — Working, Truth Table, IC 74151 and Applications

What is a Multiplexer?

A multiplexer (MUX) is a combinational circuit that selects one of 2ⁿ input lines and routes it to a single output based on n select lines.

Also called: Data Selector (it selects which data input to pass to output).

4:1 MUX

Truth Table:

Boolean expression:

8:1 MUX — IC 74151

The 74151 is a standard 8:1 multiplexer IC:

Truth Table (partial):

Implementing Boolean Functions Using MUX

A 2ⁿ:1 MUX can implement any n-variable Boolean function by connecting the truth table outputs to data inputs.

Example: Implement F(A,B,C) = Σm(1,2,4,7) using 8:1 MUX

Optimization: Use a 4:1 MUX (with 2 select variables) and the 3rd variable on data inputs:

Use A, B as selects → group minterms by A,B:

• AB=00: F = C (D0=C)
• AB=01: F = C̄ (D1=C̄)
• AB=10: F = C̄ (D2=C̄) — Wait: m4(100)=1, m5(101)=0 → D2=C̄
• AB=11: F = C (D3=C) — m6(110)=0, m7(111)=1 → D3=C

Result: 4:1 MUX with D0=C, D1=C̄, D2=C̄, D3=C

Expanding MUX

Build 16:1 MUX from two 8:1 MUX:

Verilog

Interview Questions

Q1: How many select lines does a 16:1 MUX need? log₂(16) = 4 select lines. Generally, a 2ⁿ:1 MUX needs n select lines.

Q2: What is the difference between a MUX and a decoder? A MUX selects one of multiple data inputs and routes it to a single output — it's a data selector. A decoder takes an n-bit code and activates exactly one of 2ⁿ output lines — it converts a binary code to one-hot format. MUX has data and select inputs; decoder has only address inputs.

Q3: Can any Boolean function of n variables be implemented with a 2ⁿ:1 MUX? Yes. Connect the n variables to the select lines. Each data input corresponds to one minterm. Tie each data input to 0 or 1 based on whether that minterm is in the function. A 2ⁿ:1 MUX is a universal logic element for n-variable functions.

Q4: How do you implement a 4-variable function using a 8:1 MUX? Use 3 variables as select lines. For the 4th variable (say D), express the function for each select combination in terms of D: the result is D, D̄, 0, or 1 for each data input. Connect data inputs accordingly. This is more efficient than a 16:1 MUX.

Q5: What is a tree multiplexer? A tree MUX is built by cascading smaller MUXes. For example, a 16:1 MUX can be built from 9 2:1 MUXes arranged in 4 levels, or from two 8:1 MUXes and one 2:1 MUX. The tree structure balances delay versus hardware.