Introduction:
A decoder is a logic circuit that converts coded inputs into coded outputs. It is a multiple-input, multiple-output circuit where the input and output code are different. Decoders are widely used in digital systems for various applications such as data transmission, memory addressing, and control units.

Explanation:
A decoder takes a coded input and generates an output based on the input code. The input code can be in the form of binary, Gray code, or any other coding scheme, while the output code is typically binary. The number of input lines in a decoder is determined by the number of unique input combinations or codes it can accept.

Working of a Decoder:
1. Input Lines: A decoder has multiple input lines, which are used to represent the input code. The number of input lines depends on the number of unique input codes it can handle. For example, a 3-to-8 decoder has 3 input lines, allowing it to accept 8 different input codes.

2. Enable Input: In addition to the input lines, a decoder also has an enable input. This input determines whether the decoder is active or not. When the enable input is active (usually high), the decoder processes the input and generates the corresponding output. When the enable input is inactive (usually low), the decoder does not produce any output.

3. Output Lines: The output lines of a decoder represent the output code. Each output line corresponds to a specific output code or combination. The number of output lines is determined by the number of unique output codes. For example, a 3-to-8 decoder has 8 output lines, each representing a unique output code.

4. Truth Table: The behavior of a decoder can be described using a truth table. The truth table lists all possible input codes and their corresponding output codes. It shows the relationship between the input and output of the decoder.

Applications:
Decoders are widely used in digital systems for various applications, including:
- Memory Address Decoding: Decoders are used to decode memory addresses in computer systems. They select the appropriate memory location based on the address code provided.
- Data Transmission: Decoders are used in communication systems to decode the received data. They convert the encoded data back into its original form.
- Control Units: Decoders are used in control units of digital systems to interpret control signals and generate appropriate outputs.
- Display Decoding: Decoders are used in display systems to decode the input code and activate the corresponding segments or pixels on the display.

Conclusion:
A decoder is a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs. It is widely used in digital systems for various applications. Decoders play a crucial role in data transmission, memory addressing, control units, and display systems.