Multiplexers (MUX) Demystified: The Data Traffic Controller

Denny

January 13, 2026 3 min read

Digital Logic 101

📅 January 2026 • ⏱️ 16 min read • 🎓 Beginner-Intermediate

How does a CPU choose which register to read? How does a TV select between input channels? The answer is the Multiplexer (MUX)—one of the most essential circuits in digital design. In this tutorial, you'll learn how MUX works and build one from basic gates.

What is a Multiplexer?

A multiplexer is a combinational circuit that selects one of several inputs and forwards it to a single output. Think of it as a digital switch with multiple inputs and one output—the select lines determine which input gets through.

MUX: The Data Selector

Inputs: Multiple data inputs (I₀, I₁, I₂, ...) + Select lines (S₀, S₁, ...)

Output: One output (Y) that equals the selected input

Rule: n select lines can choose from 2ⁿ inputs

A 4-to-1 multiplexer: 2 select lines choose between 4 inputs. The selected input appears at the output.

The 2-to-1 MUX

Let's start with the simplest MUX: 2-to-1. It has 2 data inputs (I₀, I₁), 1 select line (S), and 1 output (Y).

Select (S)	Output (Y)
0	Y = I₀
1	Y = I₁

The Boolean expression for a 2-to-1 MUX:

Y = S'·I₀ + S·I₁

A 2-to-1 MUX built from AND, OR, and NOT gates. When S=0, I₀ passes through; when S=1, I₁ passes through.

Scaling Up: 4-to-1 MUX

A 4-to-1 MUX has 4 data inputs and 2 select lines. The select lines form a 2-bit binary number that chooses which input to route.

S₁	S₀	Output (Y)
0	0	I₀
0	1	I₁
1	0	I₂
1	1	I₃

4-to-1 Multiplexer lesson with scaling pattern

4-to-1 MUX with function table and scaling pattern. n select lines → 2ⁿ inputs!

Key Insight: The Scaling Pattern

Multiplexers follow a simple rule: n select lines select from 2ⁿ inputs. So 1 select = 2 inputs (2:1), 2 selects = 4 inputs (4:1), 3 selects = 8 inputs (8:1), and so on.

Real-World Analogy: TV Channel Selector

Imagine you have 4 video sources (gaming console, cable box, Blu-ray, streaming stick) and one TV. A MUX is like the input selector—the remote's button (select lines) determines which source appears on screen (output).

TV Channel Selector MUX real-world analogy

TV channel selector as a MUX: select lines choose which input source appears on the TV!

Applications of Multiplexers

CPU Register File: Select which register's value to read
ALU Input Selection: Choose operands for arithmetic operations
Memory Bank Selection: Route data from different memory chips
Data Routing: Switch between different data sources
Function Generation: Implement any Boolean function with a MUX

The Demultiplexer (DEMUX)

The opposite of a MUX is a Demultiplexer (DEMUX). It takes ONE input and routes it to one of MANY outputs based on select lines.

A 1-to-4 DEMUX: one input is routed to one of four outputs based on 2 select lines.

Building an 8-to-1 MUX

Larger MUXes can be built by cascading smaller ones:

An 8-to-1 MUX with 3 select lines. This can be built from two 4-to-1 MUXes and one 2-to-1 MUX!

Try It Yourself!

Build a 2-to-1 MUX: Use 2 AND gates, 1 OR gate, and 1 NOT gate
Expand to 4-to-1: Add more AND gates and select lines
TV Selector: Wire 4 switches (channels) to a MUX
Build DEMUX: Reverse the logic—one input to multiple outputs

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