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A *demultiplexer (DEMUX)* is the inverse of a multiplexer. It takes a single input signal and routes it to one of many output lines based on a set of control or selection signals. Essentially, a demultiplexer "decodes" the incoming signal and distributes it to the appropriate output line, depending on the value of the selection lines.

Key Features:
**1 input**: The signal to be routed.
**n outputs**: Multiple output lines, with one active (usually **1**) based on the selection lines.
**Selection Lines (S₁, S₂, ..., Sₙ)**: Control lines that determine which output will receive the input signal.

How it Works:
A demultiplexer takes a single input and uses the selection lines to choose which one of its multiple output lines will carry the input signal. For example, in a **1-to-4 demultiplexer**, the 1 input will be routed to one of the 4 outputs based on the values of the 2 selection lines.

Example: 1-to-4 Demultiplexer

#### Truth Table for 1-to-4 DEMUX:

| S₁ | S₀ | Input (I) | Y₀ | Y₁ | Y₂ | Y₃ |
|----|----|-----------|----|----|----|----|
| 0 | 0 | 1 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 1 |

*S₁, S₀* are the selection lines that determine which output (Y₀, Y₁, Y₂, or Y₃) will receive the input **I**.
*S₁S₀ = 00* → Output Y₀ receives **I**.
*S₁S₀ = 01* → Output Y₁ receives **I**.
*S₁S₀ = 10* → Output Y₂ receives **I**.
*S₁S₀ = 11* → Output Y₃ receives **I**.

Types of Demultiplexers:
**1-to-2 Demux**: 1 input, 2 outputs, 1 selection line.
**1-to-4 Demux**: 1 input, 4 outputs, 2 selection lines.
**1-to-8 Demux**: 1 input, 8 outputs, 3 selection lines.
The number of selection lines needed is the logarithm base 2 of the number of outputs. For example, 2 selection lines are needed for a 1-to-4 demux, 3 for a 1-to-8 demux, and so on.

Applications:
**Data Routing**: Demuxes are used to route a single data stream to different devices or channels. For example, in communication systems where a single source sends data to multiple destinations.
**Control Systems**: Demuxes can be used to direct control signals to different parts of a system based on the selection lines.
**Memory Systems**: A demultiplexer can be used to select different memory locations or data lines from a single input.

Summary:
A *demultiplexer* is a device that takes one input signal and channels it to one of several output lines based on the values of selection lines. It is the opposite of a multiplexer, providing a way to distribute a single data stream to multiple destinations, and is used in many digital systems, including data routing, control systems, and memory addressing.