Semiconductor & Computer Engineering
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=== 4:1 Mux === | === 4:1 Mux === | ||
| + | {| class="wikitable" style="float: right;" | ||
| + | |+ 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: | 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 Q = <math>(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)</math> | + | [[File:Mux 4 1 using mux 2 1.svg|200px|center]] |
| + | |||
| + | Alternatively, a 4:1 Mux can be built out of basic gates. Its function is shown below: | ||
| + | |||
| + | Q = <math>(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)</math> | ||
Where A, B, C, and D are the four inputs. Q is the output. | Where A, B, C, and D are the four inputs. Q is the output. | ||
Revision as of 22:19, 30 December 2013
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.
Contents
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)
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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
| 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 =
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
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.
Above was 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.