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electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several
analog Analog or analogue may refer to: Computing and electronics * Analog signal, in which information is encoded in a continuous variable ** Analog device, an apparatus that operates on analog signals *** Analog electronics, circuits which use analog ...
or digital input signals and forwards the selected input to a single output line. The selection is directed by a separate set of digital inputs known as select lines. A multiplexer of 2^n inputs has n select lines, which are used to select which input line to send to the output. A multiplexer makes it possible for several input signals to share one device or resource, for example, one
analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...
or one communications
transmission medium A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulat ...
, instead of having one device per input signal. Multiplexers can also be used to implement Boolean functions of multiple variables. Conversely, a demultiplexer (or demux) is a device taking a single input and selecting signals of the output of the compatible mux, which is connected to the single input, and a shared selection line. A multiplexer is often used with a complementary demultiplexer on the receiving end. An electronic multiplexer can be considered as a multiple-input, single-output switch, and a demultiplexer as a single-input, multiple-output switch. The schematic symbol for a multiplexer is an
isosceles trapezoid In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined ...
with the longer parallel side containing the input pins and the short parallel side containing the output pin. The schematic on the right shows a 2-to-1 multiplexer on the left and an equivalent switch on the right. The sel wire connects the desired input to the output.


Applications

Multiplexers are part of computer systems to select data from a specific source, be it a memory chip or a hardware peripheral. A computer uses multiplexers to control the data and address buses, allowing the processor to select data from multiple data sources In digital communications, multiplexers allow several connections over a single channel, by connecting the multiplexer's single output to the demultiplexer's single input (Time-Division Multiplexing). The image to the right demonstrates this benefit. In this case, the cost of implementing separate channels for each data source is higher than the cost and inconvenience of providing the multiplexing/demultiplexing functions. At the receiving end of the
data link A data link is the means of connecting one location to another for the purpose of transmitting and receiving digital information (data communication). It can also refer to a set of electronics assemblies, consisting of a transmitter and a recei ...
a complementary ''demultiplexer'' is usually required to break the single data stream back down into the original streams. In some cases, the far end system may have functionality greater than a simple demultiplexer; and while the demultiplexing still occurs technically, it may never be implemented discretely. This would be the case when, for instance, 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 Routing is the process of selecting a path for traffic in a network or between or across multiple networks. Broadly, routing is performed in many types of networks, including circuit-switched networks, such as the public switched telephone netw ...
processor; and then does the demultiplexing in memory from where it will be converted directly into IP sections. Often, a multiplexer and demultiplexer are combined into a single piece of equipment, which is simply referred to as a ''multiplexer''. Both circuit elements are needed at both ends of a transmission link because most communications systems transmit in both directions. In
analog circuit Analogue electronics ( en-US, analog electronics) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relati ...
design, a multiplexer is a special type of analog switch that connects one signal selected from several inputs to a single output.


Digital multiplexers

In digital circuit design, the selector wires are of digital value. In the case of a 2-to-1 multiplexer, a logic value of 0 would connect I_0 to the output while a logic value of 1 would connect I_1 to the output. In larger multiplexers, the number of selector pins is equal to \left \lceil \log_2(n) \right \rceil where n is the number of inputs. For example, 9 to 16 inputs would require no fewer than 4 selector pins and 17 to 32 inputs would require no fewer than 5 selector pins. The binary value expressed on these selector pins determines the selected input pin. A 2-to-1 multiplexer has a
boolean equation In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in ...
where A and B are the two inputs, S_0 is the selector input, and Z is the output: : Z = ( A \wedge \neg S_0) \vee (B \wedge S_0) Which can be expressed as a
truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional argumen ...
: Or, in simpler notation: These tables show that when S_0 = 0 then Z = A but when S_0 = 1 then Z = B. A straightforward realization of this 2-to-1 multiplexer would need 2 AND gates, an OR gate, and a NOT gate. While this is mathematically correct, a direct physical implementation would be prone to
race condition A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of t ...
s that require additional gates to suppress. Larger multiplexers are also common and, as stated above, require \left \lceil \log_2(n) \right \rceil selector pins for n inputs. Other common sizes are 4-to-1, 8-to-1, and 16-to-1. Since digital logic uses binary values, powers of 2 are used (4, 8, 16) to maximally control a number of inputs for the given number of selector inputs. File:Multiplexer 4-to-1.svg, 4-to-1 mux File:Multiplexer 8-to-1.svg, 8-to-1 mux File:Multiplexer 16-to-1.svg, 16-to-1 mux The boolean equation for a 4-to-1 multiplexer is: :Z = (A \wedge \neg \wedge \neg S_1) \vee (B \wedge S_0 \wedge \neg S_1) \vee (C \wedge \neg S_0 \wedge S_1) \vee (D \wedge S_0 \wedge S_1) The following 4-to-1 multiplexer is constructed from 3-state buffers and AND gates (the AND gates are acting as the decoder): The subscripts on the I_n inputs indicate the decimal value of the binary control inputs at which that input is let through.


Chaining multiplexers

Larger Multiplexers can be constructed by using smaller multiplexers by chaining them together. For example, an 8-to-1 multiplexer can be made with two 4-to-1 and one 2-to-1 multiplexers. The two 4-to-1 multiplexer outputs are fed into the 2-to-1 with the selector pins on the 4-to-1's put in parallel giving a total number of selector inputs to 3, which is equivalent to an 8-to-1.


List of ICs which provide multiplexing

For
7400 series The 7400 series of integrated circuits (ICs) are a popular logic family of transistor–transistor logic (TTL) logic chips. In 1964, Texas Instruments introduced the SN5400 series of logic chips, in a ceramic semiconductor package. A lo ...
part numbers in the following table, "x" is the logic family.


Digital demultiplexers

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. Demultiplexers are sometimes convenient for designing general-purpose logic because if the demultiplexer's input is always true, the demultiplexer acts as a
binary decoder In digital electronics, a binary decoder is a combinational logic circuit that converts binary information from the n coded inputs to a maximum of 2n unique outputs. They are used in a wide variety of applications, including instruction decoding ...
. This means that any function of the selection bits can be constructed by logically OR-ing the correct set of outputs. If X is the input and S is the selector, and A and B are the outputs: A = ( X \wedge \neg S) B = ( X \wedge S)


List of ICs which provide demultiplexing

For
7400 series The 7400 series of integrated circuits (ICs) are a popular logic family of transistor–transistor logic (TTL) logic chips. In 1964, Texas Instruments introduced the SN5400 series of logic chips, in a ceramic semiconductor package. A lo ...
part numbers in the following table, "x" is the logic family.


Multiplexers as PLDs

Multiplexers can also be used as
programmable logic device A programmable logic device (PLD) is an electronic component used to build reconfigurable digital circuits. Unlike digital logic constructed using discrete logic gates with fixed functions, a PLD has an undefined function at the time of manu ...
s, to implement Boolean functions. Any Boolean function of ''n'' variables and one result can be implemented with a multiplexer with ''n'' selector inputs. The variables are connected to the selector inputs, and the function result, 0 or 1, for each possible combination of selector inputs is connected to the corresponding data input. If one of the variables (for example, ''D'') is also available inverted, a multiplexer with ''n''-1 selector inputs is sufficient; the data inputs are connected to 0, 1, ''D'', or ~''D'', according to the desired output for each combination of the selector inputs.


See also

* Digital subscriber line access multiplexer (DSLAM) *
Inverse multiplexer An inverse multiplexer (often abbreviated to inverse MUX or IMUX) allows a data stream to be broken into multiple lower data rate communication links. An inverse multiplexer differs from a demultiplexer because the multiple output streams from ...
*
Multiplexing In telecommunications and computer networking, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource - a ...
**
Code-division multiplexing Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies. CDMA is an example of multiple access, where several transmitters can send information simultaneously over a single communication ...
**
Frequency-division multiplexing In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency bands, each of which is used to carry a separat ...
**
Time-division multiplexing Time-division multiplexing (TDM) is a method of transmitting and receiving independent signals over a common signal path by means of synchronized switches at each end of the transmission line so that each signal appears on the line only a fracti ...
** Wavelength-division multiplexing **
Statistical multiplexing Statistical multiplexing is a type of communication link sharing, very similar to dynamic bandwidth allocation (DBA). In statistical multiplexing, a communication channel is divided into an arbitrary number of variable bitrate digital channels or ...
**
Charlieplexing Charlieplexing (also known as tristate multiplexing, reduced pin-count LED multiplexing, complementary LED drive and crossplexing) is a technique for driving a multiplexed display in which relatively few I/O pins on a microcontroller are used ...
*
Priority encoder A priority encoder is a circuit or algorithm that compresses multiple binary inputs into a smaller number of outputs. The output of a priority encoder is the binary representation of the index of the most significant activated line, starting from ...
*
Rule 184 Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems: * Rule 184 can be used as a simpl ...
, a
cellular automaton A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tesse ...
in which each cell acts as a multiplexer for the values from the two adjacent cells *
Statistical multiplexer Statistical multiplexing is a type of communication link sharing, very similar to dynamic bandwidth allocation (DBA). In statistical multiplexing, a communication channel is divided into an arbitrary number of variable bitrate digital channels or ...


References


Further reading

*


External links

* {{Authority control Multiplexing Digital circuits