Multiplexer

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In electronics, a multiplexer (or mux) is a device that selects between several analog or digital input signals and forwards it to a single output line. [1] A multiplexer of ${\displaystyle 2^{n}}$ inputs has ${\displaystyle n}$ select lines, which are used to select which input line to send to the output. [2] Multiplexers are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth. [1] A multiplexer is also called a data selector. Multiplexers can also be used to implement Boolean functions of multiple variables.

Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter.

An analog signal is any continuous signal for which the time-varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves. It differs from a digital signal, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values. The term analog signal usually refers to electrical signals; however, mechanical, pneumatic, hydraulic, human speech, and other systems may also convey or be considered analog signals.

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency.

Contents

An electronic multiplexer makes it possible for several signals to share one device or resource, for example, one A/D converter or one communication line, instead of having one device per input signal.

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. [1]

An electronic multiplexer can be considered as a multiple-input, single-output switch, and a demultiplexer as a single-input, multiple-output switch. [3] The schematic symbol for a multiplexer is an isosceles trapezoid with the longer parallel side containing the input pins and the short parallel side containing the output pin. [4] The schematic on the right shows a 2-to-1 multiplexer on the left and an equivalent switch on the right. The ${\displaystyle sel}$ wire connects the desired input to the output.

In Euclidean geometry, an isosceles trapezoid 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 as a trapezoid in which both legs and both base angles are of the same measure. Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry. In any isosceles trapezoid, two opposite sides are parallel, and the two other sides are of equal length. The diagonals are also of equal length. The base angles of an isosceles trapezoid are equal in measure.

Cost saving

One use for multiplexers is economizing connections over a single channel, by connecting the multiplexer's single output to the demultiplexer's single input. 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 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 typical when: 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 sections.

In telecommunication a data link is the means of connecting one location to another for the purpose of transmitting and receiving digital information. It can also refer to a set of electronics assemblies, consisting of a transmitter and a receiver and the interconnecting data telecommunication circuit. These are governed by a link protocol enabling digital data to be transferred from a data source to a data sink.

The Internet Protocol (IP) is the principal communications protocol in the Internet protocol suite for relaying datagrams across network boundaries. Its routing function enables internetworking, and essentially establishes the Internet.

A router is a networking device that forwards data packets between computer networks. Routers perform the traffic directing functions on the Internet. Data sent through the internet, such as a web page or email, is in the form of data packets. A packet is typically forwarded from one router to another router through the networks that constitute an internetwork until it reaches its destination node.

Often, a multiplexer and demultiplexer are combined together into a single piece of equipment, which is conveniently 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.

A duplex communication system is a point-to-point system composed of two or more connected parties or devices that can communicate with one another in both directions. Duplex systems are employed in many communications networks, either to allow for simultaneous communication in both directions between two connected parties or to provide a reverse path for the monitoring and remote adjustment of equipment in the field. There are two types of duplex communication systems: full-duplex (FDX) and half-duplex (HDX).

In analog circuit 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 ${\displaystyle \scriptstyle I_{0}}$ to the output while a logic value of 1 would connect ${\displaystyle \scriptstyle I_{1}}$ to the output. In larger multiplexers, the number of selector pins is equal to ${\displaystyle \scriptstyle \left\lceil \log _{2}(n)\right\rceil }$ where ${\displaystyle \scriptstyle n}$ 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 where ${\displaystyle \scriptstyle A}$ and ${\displaystyle \scriptstyle B}$ are the two inputs, ${\displaystyle \scriptstyle S_{0}}$ is the selector input, and ${\displaystyle \scriptstyle Z}$ is the output:

${\displaystyle Z=(A\wedge \neg S_{0})\vee (B\wedge S_{0})}$

Which can be expressed as a truth table:

${\displaystyle \scriptstyle S_{0}}$${\displaystyle \scriptstyle A}$${\displaystyle \scriptstyle B}$${\displaystyle \scriptstyle Z}$
0000
0010
0101
0111
1000
1011
1100
1111

Or, in simpler notation:

${\displaystyle \scriptstyle S_{0}}$${\displaystyle \scriptstyle Z}$
0A
1B

These tables show that when ${\displaystyle \scriptstyle S_{0}=0}$ then ${\displaystyle \scriptstyle Z=A}$ but when ${\displaystyle \scriptstyle S_{0}=1}$ then ${\displaystyle \scriptstyle Z=B}$. 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 conditions that require additional gates to suppress. [5]

Larger multiplexers are also common and, as stated above, require ${\displaystyle \scriptstyle \left\lceil \log _{2}(n)\right\rceil }$ selector pins for ${\displaystyle n}$ 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.

The boolean equation for a 4-to-1 multiplexer is:

${\displaystyle Z=(A\wedge \neg {S_{0}}\wedge \neg S_{1})\vee (B\wedge S_{0}\wedge \neg S_{1})\vee (C\wedge \neg S_{0}\wedge S_{1})\vee (D\wedge S_{0}\wedge S_{1})}$

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 ${\displaystyle \scriptstyle I_{n}}$ 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

The 7400 series has several ICs that contain multiplexer(s):

IC No.FunctionOutput State
74157Quad 2:1 mux.Output same as input given
74158Quad 2:1 mux.Output is inverted input
74153Dual 4:1 mux.Output same as input
74352Dual 4:1 mux.Output is inverted input
74151A8:1 mux.Both outputs available (i.e., complementary outputs)
741518:1 mux.Output is inverted input
7415016:1 mux.Output is inverted input

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 decoder. 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:

${\displaystyle A=(X\wedge \neg S)}$

${\displaystyle B=(X\wedge S)}$

List of ICs which provide demultiplexing

The 7400 series has several ICs that contain demultiplexer(s):

IC No. (7400)IC No. (4000)FunctionOutput State
74139Dual 1:4 demux.Output is inverted input
74156Dual 1:4 demux.Output is open collector
741381:8 demux.Output is inverted input
742381:8 demux.
741541:16 demux.Output is inverted input
74159CD4514/151:16 demux.Output is open collector and same as input

Multiplexers as PLDs

Multiplexers can also be used as programmable logic devices, specifically 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. This is especially useful in situations when cost is a factor, for modularity, and for ease of modification. 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. [6]

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References

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