Multiplexer (MUX)
Introduction
A Multiplexer (MUX) is a digital combinational circuit that accepts multiple input signals but allows only one of them to pass through the output at any given time. In simple terms, it performs a one-out-of-N selection, where N = 2ⁿ, based on the values of the select lines.
Because of this selection property, a multiplexer is also called a data selector. It acts like an electronic switch whose path is controlled by binary select inputs.
The block diagram of a general 2ⁿ:1 multiplexer is shown below:
- Inputs: I₀, I₁, …, I₂ⁿ⁻¹
- Select lines: n control bits
- Output: One output line (Y)
The select lines determine which input line is connected to the output.
Working Principle
The multiplexer works like a switch:
- If the select lines hold a particular binary combination, the corresponding input is connected to the output.
- For example, in a 4:1 multiplexer, when the select lines S₁S₀ = 10, the input I₂ is transmitted to the output.
Thus, the multiplexer allows data sharing between multiple input sources and a single communication line.
Types of Multiplexers
1. 2×1 Multiplexer
- Inputs: I₀, I₁
- Select line: S
- Output: Y
| Select Line (S) | Output (Y) |
|---|---|
| 0 | I₀ |
| 1 | I₁ |
The Boolean expression for the output is:
Y = S′·I₀ + S·I₁
2. 4×1 Multiplexer
- Inputs: I₀, I₁, I₂, I₃
- Select lines: S₁, S₀
- Output: Y
| S₁ | S₀ | Output (Y) |
|---|---|---|
| 0 | 0 | I₀ |
| 0 | 1 | I₁ |
| 1 | 0 | I₂ |
| 1 | 1 | I₃ |
Boolean equation:
Y = S₁′S₀′I₀ + S₁′S₀I₁ + S₁S₀′I₂ + S₁S₀I₃
This circuit can be built using AND, OR, and NOT gates.
3. 8×1 Multiplexer (Using 4×1 and 2×1 MUX)
- Inputs: I₀ to I₇
- Select lines: S₂, S₁, S₀
- Output: Y
Working:
- Two 4×1 MUX are used in the first stage (handling I₀–I₃ and I₄–I₇).
- Their outputs are connected to a 2×1 MUX in the second stage.
- The select line S₂ decides which 4×1 MUX output goes to the final output.
Truth table:
| S₂ | S₁ | S₀ | Output (Y) |
|---|---|---|---|
| 0 | 0 | 0 | I₀ |
| 0 | 0 | 1 | I₁ |
| 0 | 1 | 0 | I₂ |
| 0 | 1 | 1 | I₃ |
| 1 | 0 | 0 | I₄ |
| 1 | 0 | 1 | I₅ |
| 1 | 1 | 0 | I₆ |
| 1 | 1 | 1 | I₇ |
4. 16×1 Multiplexer (Using 8×1 and 2×1 MUX)
- Inputs: I₀ to I₁₅
- Select lines: S₃, S₂, S₁, S₀
- Output: Y
Working:
- Two 8×1 MUX are used in the first stage (I₀–I₇ and I₈–I₁₅).
- A 2×1 MUX is used in the second stage to select between them, controlled by S₃.
Applications of Multiplexers
-
Data routing in communication systems.
-
Parallel-to-serial conversion in data transmission.
-
Implementation of Boolean functions using MUX logic.
-
Signal generation and waveform selection in digital circuits.
-
Used in computer processors, control systems, and memory addressing.
Conclusion
A multiplexer is an essential combinational logic device that selects one input from several and forwards it to the output. It is widely used in digital systems for data selection, routing, and logic implementation. Higher-order multiplexers (8×1, 16×1, etc.) can be built using smaller multiplexers like 2×1 and 4×1, making MUX design highly scalable.
No comments:
Post a Comment