Multiplexer

A multiplexer combines two or more inputs into a single output. In electronics, the multiplexer or mux combines several electrical signals into a single signal. There are different types of multiplexers for analog and digital circuits.

In digital signal processing, the multiplexer (often abbreviated to mux or, more rarely, muldex) takes several separate digital data streams and combines them together into one data stream of a higher data rate. This allows multiple data streams to be carried from one place to another over one physical link, which saves cost.

At the receiving end of the data link a complementary demultiplexer or demux is normally required to break the high data rate stream back down into the original lower rate streams. In some cases, the far end system may have more functionality than a simple demultiplexer and so, whilst the demultiplexing still exists logically, it may never actually happen physically. This would be typical where a multiplexer serves a number of IP network users and then feeds directly into a router which immediately reads the content of the entire link into its routing processor and then does the demultiplexing in memory from where it will be converted directly into IP packets.

It is usual to combine a multiplexer and a demultiplexer together into one piece of equipment and simply refer to the whole thing as a "multiplexer". Both pieces of equipment are needed at both ends of a transmission link because most communications systems transmit in both directions.

A real world example is the creation of telemetry for transmission from the computer/instrumentation system of a satellite, space craft or other remote vehicle to a ground system.

In digital circuit design, the multiplexer is a device that has multiple input streams and only one output stream. It forwards one of the input streams to the output stream based on the values of one or more "selection inputs" . For example, a two-input multiplexer is a simple connection of logic gates whose output Y is either input A or input B depending on the value of a third input S which selects the input. Its boolean equation is:

Y = (A and S) or (B and not S)

which can be expressed as the truth table:

A B S | Y
------+--
0 0 0 | 0 (pick B)
0 0 1 | 0 (pick A)
0 1 0 | 1 (pick B)
0 1 1 | 0 (pick A)
1 0 0 | 0 (pick B)
1 0 1 | 1 (pick A)
1 1 0 | 1 (pick B)
1 1 1 | 1 (pick A)

or as the Karnaugh map:

Y        S
      | 0 1
   ---+-----  
AB 00 | 0 0
   01 | 1 0
   11 | 1 1
   10 | 0 1

Larger multiplexers are also common. For example, an 8-input multiplexer has eight data inputs and three selection inputs. The data inputs are numbered X₀ through X₇, and the selection inputs are numbered S₄, S₂, and S₁. If S₄ and S₁ are true, and S₂ is false, for example, the output will be equal to X₅.

Demultiplexers take one data input and a number of selection inputs, and they have several outputs. They forward the data input to one of the outputs depending on the values of the selection inputs. For example, an 8-output demultiplexer has one data input (X), three selection inputs (S₄, S₂, and S₁), and eight data outputs (A₀ through A₇). If S₄ and S₁ are true, and S₂ is false, for example, the output A_{5_{will be equal to X, and all other outputs are equal to zero regardless of the value of X. Demultiplexers are sometimes convenient for designing general purpose logic, because if the demultiplexer's input is always true, the demultiplexer acts as a decoder. This means that any function of the selection bits can be constructed by logically OR-ing the correct set of outputs.}}

In analogue circuit design, a multiplexer is a special type of analogue switch that connects one signal selected from several inputs to a single output.

See also