🧠 Introduction
A Multiplexer (MUX) is a combinational logic circuit that selects one input from multiple inputs and forwards it to a single output line.
👉 Think of a Multiplexer as a digital switch that connects one input out of many inputs to the output based on control signals.
Thus, it reduces multiple data lines into one — saving communication lines.
🎯 Purpose of Multiplexer
- To select and transmit one signal out of several inputs.
- To reduce the number of data lines needed in digital communication.
- Efficiently manage large data transfers using fewer wires.
⚙️ Working Principle
A Multiplexer works on:
- 2ⁿ input lines
- n selection lines (control signals)
- 1 output line
The selection lines determine which input is connected to the output.
🛠️ Basic Structure
| No. of Inputs | No. of Select Lines | Example |
|---|---|---|
| 2 | 1 | 2×1 MUX |
| 4 | 2 | 4×1 MUX |
| 8 | 3 | 8×1 MUX |
| 16 | 4 | 16×1 MUX |
In general:
For m inputs, you need n select lines, where m = 2ⁿ.
📈 Block Diagram of a Multiplexer
Here’s the simple block-level structure:
Inputs: I₀, I₁, I₂, ..., Iₙ
|
Select Lines (S₀, S₁, ..., Sn)
|
[ MUX ]
|
Output (Y)
The select lines decide which input (I₀, I₁, I₂, etc.) will appear at the output (Y).
📑 Example: 4×1 Multiplexer
- Inputs: I₀, I₁, I₂, I₃
- Select lines: S₁, S₀
- Output: Y
Truth Table:
| S₁ | S₀ | Output Y |
|---|---|---|
| 0 | 0 | I₀ |
| 0 | 1 | I₁ |
| 1 | 0 | I₂ |
| 1 | 1 | I₃ |
✅ So based on S₀ and S₁ values, one of I₀, I₁, I₂, or I₃ is passed to the output.
🧩 Circuit Diagram of 4×1 MUX
Logical Expression for Output Y:
Y = (I₀ AND ~S₁ AND ~S₀) OR (I₁ AND ~S₁ AND S₀) OR (I₂ AND S₁ AND ~S₀) OR (I₃ AND S₁ AND S₀)
where:
- ‘~’ means NOT (inverted)
This expression is implemented using AND, OR, and NOT gates.
🧠 Important Points
- A MUX reduces complexity in circuits by limiting the number of required paths.
- Selection lines are very important — they control which input appears at the output.
- Multiplexers are sometimes called “Data Selectors” because they select data.
🌟 Applications of Multiplexer
| Application | How it’s used |
|---|---|
| Data Routing | Sending one of several data sources through a single line |
| Communication Systems | Transmitting different signals over a single channel |
| Arithmetic Units | Selecting various operations based on user command |
| Computer Memory | Reading multiple memory locations |
| Control Systems | Channeling control signals |
🔥 Advantages of Multiplexer
- Saves wiring cost by reducing the number of data lines.
- Simplifies circuit design.
- Efficient use of hardware.
- Flexible control using select lines.
🎯 Summary
| Feature | Multiplexer |
|---|---|
| Purpose | Select one input from many |
| Output Lines | Only 1 |
| Input Lines | 2ⁿ inputs |
| Control Signals | n select lines |
| Major Component Used | AND, OR, NOT gates |
✏️ Example Problem
👉 Design a 4×1 Multiplexer.
Inputs: I₀, I₁, I₂, I₃
Select Lines: S₁, S₀
Output Y:
Y = (I₀ ⋅ ¬S₁ ⋅ ¬S₀) + (I₁ ⋅ ¬S₁ ⋅ S₀) + (I₂ ⋅ S₁ ⋅ ¬S₀) + (I₃ ⋅ S₁ ⋅ S₀)
where (⋅) = AND, (+) = OR, (¬) = NOT
✅ Implement using basic gates!
🎯 Types of Multiplexers
| MUX Type | Description |
|---|---|
| 2×1 MUX | 2 inputs, 1 select line |
| 4×1 MUX | 4 inputs, 2 select lines |
| 8×1 MUX | 8 inputs, 3 select lines |
| 16×1 MUX | 16 inputs, 4 select lines |
(and so on)
📢 Real-Life Analogy
Think of a Multiplexer like a railway track switch 🚂:
- Many trains (inputs) are coming.
- A switch (select line) chooses which train goes onto the single track (output).