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What is multiplexer and demultiplexer?

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### Multiplexer (MUX)

A **multiplexer (MUX)** is a digital electronic device that selects one of many input signals and forwards the selected input to a single output line. It works like a "data selector," allowing multiple data sources to share a single transmission line.

A multiplexer is often described by the number of data input lines it has and the number of selection lines needed to choose between those data lines. For example, a **4-to-1 multiplexer** has 4 data inputs, 1 output, and 2 selection lines (since \(2^2 = 4\) gives the number of selection lines needed to choose among 4 inputs).

#### Basic Working of a Multiplexer:
- A multiplexer has multiple input lines, one output line, and several selection lines (control lines).
- The selection lines determine which input signal is connected to the output.
- Based on the value of the selection lines, one of the input lines is passed to the output.

#### Example:
For a **2-to-1 multiplexer**:
- It has **2 input lines** (let's say I0 and I1), **1 output line** (Y), and **1 control line** (S).
- If \(S = 0\), the output \(Y = I0\).
- If \(S = 1\), the output \(Y = I1\).

This allows you to select between two inputs using the control signal.

### Demultiplexer (DEMUX)

A **demultiplexer (DEMUX)**, on the other hand, is the reverse of a multiplexer. It takes a single input signal and routes it to one of many output lines, based on the values of its selection lines. In essence, a demultiplexer "spreads" data from one source to multiple destinations.

#### Basic Working of a Demultiplexer:
- A demultiplexer has **1 input line**, multiple **output lines**, and several **selection lines**.
- The selection lines are used to determine which output line the input signal is connected to.
- Based on the value of the selection lines, the input is passed to one of the output lines.

#### Example:
For a **1-to-4 demultiplexer**:
- It has **1 input line** (let's say I), **4 output lines** (O0, O1, O2, O3), and **2 selection lines** (S1 and S0).
- If \(S1S0 = 00\), the input \(I\) is routed to \(O0\).
- If \(S1S0 = 01\), the input \(I\) is routed to \(O1\).
- If \(S1S0 = 10\), the input \(I\) is routed to \(O2\).
- If \(S1S0 = 11\), the input \(I\) is routed to \(O3\).

### Differences Between Multiplexer and Demultiplexer:

| **Multiplexer (MUX)**         | **Demultiplexer (DEMUX)**      |
|-------------------------------|--------------------------------|
| Takes multiple inputs and selects one. | Takes one input and distributes it to multiple outputs. |
| It has **multiple inputs** and **one output**. | It has **one input** and **multiple outputs**. |
| Selection lines control which input is connected to the output. | Selection lines control to which output the input is routed. |
| Used for efficient data transmission and resource sharing. | Used for splitting a single signal into multiple channels. |

### Applications:
- **Multiplexer** is used in communication systems, data routing, and reducing the number of transmission lines.
- **Demultiplexer** is used in applications like broadcasting, signal distribution, and communication networks where data needs to be split into multiple channels for further processing.

In summary, while the multiplexer combines multiple signals into one, the demultiplexer separates one signal into many, making them complementary in digital systems.
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