Multiplexers, Decoders, and Encoders

A multiplexer, or mux, is a combinational circuit that selects binary information from one of many input lines and directs it to a single output line.
It works like a digitally controlled multi-way switch where the binary data from multiple input lines is directed to a single output.
The selection of a particular input line is controlled by a set of selection lines. Typically, a multiplexer with n selection lines has 2^n input lines.
A multiplexer is commonly used in data routing, communication, data processing and transmission applications.
The reverse of a multiplexer is a demultiplexer, which takes a single input line and routes it to one of multiple output lines.
An important use of multiplexers is in implementing Boolean functions, which can be done by storing the function’s truth table in the multiplexer’s data inputs.

A decoder is a combinational circuit that converts binary information from n encoded inputs to a maximum of 2^n unique outputs.
They are used in a variety of devices and applications, such as data multiplexing, memory address decoding, and 7-segment displays.
A key use for decoders is in demultiplexing applications where data needs to be routed from one line to one of many lines.
With the addition of enable inputs, we can control whether the decoder is active or not, adding further versatility to its uses.
Apart from their use in digital systems, decoder circuits are also widely used in communication systems for error detection and correction.

An encoder is a combinational circuit that converts information from one format to another. Specifically, it converts multiple inputs into a binary code.
It performs the inverse operation of a decoder, taking 2^n or fewer number of inputs, and encoding it into an n-bit code.
An encoder has 2^n (or fewer) input lines, and n output lines. From this, it can generate a binary code corresponding to the input value.
Encoders are used in a number of different types of applications, including data compression, error detection and correction schemes, and in the generation of parity bits in parity check codes.
Encoders can be categorised as either priority encoders or non-priority encoders depending on how they handle inputs.
A limitation of encoders is that they consider all inputs equally likely. They tend to be less efficient when the input probabilities are not equal. If the inputs have unequal probabilities, a more efficient encoding method can be achieved with Huffman coding.