A multiplexer (mux) is a digital device that selects one of its inputs and connects it to its output. A set of inputs called select lines determine which input should be passed to the output. A multiplexer is unidirectional - the flow is only from input to output.
Multiplexers are useful in any application in which data must be chosen from multiple sources to a single destination. Multiplexers are also heavily used in I/O operations, data buses, and register files.
A multiplexer with 2N input lines requires N select lines.
A typical example of a multiplexer is shown on the right. When Sel is 0, Q = I1. When Sel is 1, Q = I2.
It's often desirable to add an enable input EN to a multiplexer. An enable input makes the multiplexer operate. When EN = 0, the output is 0. When EN = 1, the multiplexer performs its operation depending on the selection line.
Many different variations of multiplexers exist.
 2:1 Mux
 4:1 Mux
A 4:1 Multiplexer is a common multiplexer that takes selects one input among 4 and connects it to its output based on a 2-bit select line. There are many way to construct a 4:1 Mux, one possibility is using 2:1 Mux as shown below:
Alternatively, a 4:1 Mux can be built out of basic gates. Its function is shown below:
Q = \((A \land \overline S_0 \land \overline S_1) \lor (B \land \overline S_0 \land S_1) \lor (C \land S_0 \land \overline S_1) \lor (D \land S_0 \land S_1)\)
Where A, B, C, and D are the four inputs. Q is the output.
 Larger Multiplexers
Multiplexers generally only come in a few common sizes. Even in ASIC design, arbitrary sized multiplexers are not always offered. Large multiplexers can always be built from a collection of smaller ones. Consider a register file with 32 registers where we only want to select a single register at any given time. Such multiplexer can be design from four 8:1 Mux.
 74151 - 8:1 Mux
To the right is the typical schematic of the 74151, 16-pin DIP IC. Vcc is on pin 16 and GND is on pin 8. Pins 5 and 6 are the outputs, the output on pin 6 is the inverted version of the output on pin 5. The enable is on pin 7.
 Tri-State Outputs
Some commercial multiplexers have tri-state outputs. When the EN input is LOW, instead of the output being forced into 0, it gets forced into a Hi-Z state.