# Multiplexer

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.

##  Enable

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.

##  Variations

May different variations of multiplexers exit.

###  2:1 Mux

A 2:1 Mux is the simplest multiplexer that can be made. Its selection lines is made of a single bit. A truth table is provided on the right. The logic function of a 2:1 Mux is: Q=(A ∧ S) ∨ (B ∧ S)

2:1 Mux
Sel A B Q
0 0 X 0
0 1 X 1
1 X 0 0
1 X 1 1

Very fast, CMOS-based, 2:1 Mux devices can be built using two transmission gates as shown below. Note that the implementation below is a nonrestoring multiplexer.

###  4:1 Mux

4:1 Mux
Sel<0> Sel<1> I<0> I<1> I<2> I<3> Q
0 0 0 X X X 0
0 0 1 X X X 0
0 0 1 X X X 1
0 1 X 0 X X 0
0 1 X 1 X X 1
1 0 X X 0 X 0
1 0 X X 1 X 1
1 1 X X X 1 0
1 1 X X X 0 1

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

74151 IC Chip

A common multiplexer is the 8:1 Mux which selects one of 8 bits of input. The 74151 is a popular 16-pin DIP IC that implements an 8:1 mux. Note that the implementation below is an active-low.

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.

8:1 Mux
Inputs Output
Select Enable
Sel<0> Sel<1> Sel<2> EN Q Q
X X X 1 1 0
0 0 0 0 I<0> I<0>
0 0 1 0 I<1> I<1>
0 1 0 0 I<2> I<2>
0 1 1 0 I<3> I<3>
1 0 0 0 I<4> I<4>
1 0 1 0 I<5> I<5>
1 1 0 0 I<6> I<6>
1 1 1 0 I<7> I<7>
74151 IC 8:1 MUX

##  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.