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| {{About|electronic switching|telecommunications|multiplexing}}
| | I am Damaris from Paudex doing my final year engineering in Architecture. I did my schooling, secured 71% and hope to find someone with same interests in Poker.<br><br>Check out my web site: [http://www.womenscenter.com First Trimester Abortion Clinics Florida] |
| [[File:Multiplexer2.png|thumb|300px|right|Schematic of a 2-to-1 Multiplexer. It can be equated to a controlled switch.]]
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| [[File:Demultiplexer.png|thumb|270px|right|Schematic of a 1-to-2 Demultiplexer. Like a multiplexer, it can be equated to a controlled switch.]]
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| In [[electronics]], a '''multiplexer''' (or '''mux''') is a device that selects one of several [[Analog signal|analog]] or [[Digital signal|digital]] input signals and forwards the selected input into a single line.<ref name="Network+ Guide to Networks">{{cite book | last = Dean | first = Tamara | title = Network+ Guide to Networks | publisher = Delmar | year = 2010 | location = | pages = 82–85 | url = http://books.google.com/books?id=UD0h_GqgbHgC&printsec=frontcover&dq=network%2B+guide+to+networks&src=bmrr#v=onepage&q&f=false}}</ref> A multiplexer of 2<sup>''n''</sup> inputs has ''n'' select lines, which are used to select which input line to send to the output.<ref>{{cite book | last = Debashis | first = De | title = Basic Electronics | publisher = Dorling Kindersley | year = 2010 | location = | pages = 557 | url = http://books.google.com/books?id=mT_j4F1bJx4C&printsec=frontcover&dq=Basic+Electronics+By+De+Debashis#v=onepage&q&f=false}}</ref> Multiplexers are mainly used to increase the amount of data that can be sent over the [[Computer network|network]] within a certain amount of time and [[Bandwidth (signal processing)|bandwidth]].<ref name="Network+ Guide to Networks"/> A multiplexer is also called a '''data selector'''.
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| 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.
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| Conversely, a '''demultiplexer''' (or '''demux''') is a device taking a single input signal and selecting one of many data-output-lines, which is connected to the single input. A multiplexer is often used with a complementary demultiplexer on the receiving end.<ref name="Network+ Guide to Networks"/>
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| An electronic multiplexer can be considered as a [[MISO#Characterization_of_systems|multiple-input, single-output]] switch, and a demultiplexer as a [[MISO#Characterization_of_systems|single-input, multiple-output]] switch.<ref>{{cite book | last = Lipták | first = Béla | title = Instrument engineers' handbook: Process software and digital networks | publisher = CRC Press | year = 2002 | location = | pages = 343 | url = http://books.google.com/books?id=KPjLAyA7HgoC&printsec=frontcover&dq=instrument+engineers'+handbook:+Process+software+and+digital+networks+By+B%C3%A9la+G.+Lipt%C3%A1k#v=onepage&q&f=false}}</ref> 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.<ref>{{cite book | last = Harris | first = David | title = Digital Design and Computer Architecture | publisher = Penrose | year = 2007 | location = | pages = 79 | url = http://books.google.com/books?id=5X7JV5-n0FIC&printsec=frontcover&dq=Digital+design+and+computer+architecture+By+David+Money+Harris,+Sarah+L.+Harris#v=onepage&q&f=false}}</ref> The schematic on the right shows a 2-to-1 multiplexer on the left and an equivalent switch on the right. The <math>sel</math> wire connects the desired input to the output.
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| ==Telecommunications==
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| {{Main|Multiplexing}}
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| In [[telecommunications]], a multiplexer is a device that combines several input information signals into one output signal, which carries several [[communication channel]]s, by means of some [[multiplexing|multiplex technique]]. A '''demultiplexer''' is, in this context, a device taking a single input signal that carries many channels and separates those over multiple output signals.
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| {{Multiplex techniques}}
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| In telecommunications and [[signal processing]], an analog [[time division multiplexing|time division multiplexer]] (TDM) may take several samples of separate analogue signals and combine them into one wide-band analog signal. Alternatively, a digital TDM may combine a limited number of constant [[bit rate]] digital [[data stream]]s into one data stream of a higher data rate, by forming [[Frame (networking)|data frames]] consisting of one timeslot per channel.
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| In telecommunications, [[computer networks]] and [[digital video]], a [[statistical multiplexer]] may combine several variable bit rate data streams into one constant bandwidth signal, for example by means of [[packet mode]] communication. An [[inverse multiplexer]] may utilize several communication channels for transferring one signal.Multipliexer has many inputs and limited outputs on the other hand demultipliexer has many outputs and limited inputs.
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| ==Cost saving==
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| [[File:Telephony multiplexer system.gif|thumb|right|300px|The basic function of a multiplexer: combining multiple inputs into a single data stream. On the receiving side, a demultiplexer splits the single data stream into the original multiple signals.]]
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| One use for multiplexers is cost saving by connecting a multiplexer and a '''demultiplexer''' (or '''demux''') together over a single channel (by connecting the multiplexer's single output to the demultiplexer's single input).
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| The image to the right demonstrates this.
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| 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.
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| At the receiving end of the [[data link]] a complementary ''demultiplexer'' is normally required to break single data stream back down into the original streams.
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| In some cases, the far end system may have more functionality than a simple demultiplexer and so, while the demultiplexing still exists logically, it may never actually happen physically.
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| This would be typical where a multiplexer serves a number of [[Internet Protocol|IP]] network users and then feeds directly into a [[router (computing)|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.
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| Often, a multiplexer and demultiplexer are combined together into a single piece of equipment, which is usually referred to simply as a "multiplexer". Both pieces of equipment are needed at both ends of a transmission link because most communications systems transmit in [[Duplex (telecommunications)|both directions]].
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| 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.
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| ==Digital multiplexers==
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| 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 <math>\scriptstyle I_0</math> to the output while a logic value of 1 would connect <math>\scriptstyle I_1</math> to the output.
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| In larger multiplexers, the number of selector pins is equal to <math>\scriptstyle \left \lceil \log_2(n) \right \rceil</math> where <math>\scriptstyle n</math> is the number of inputs.
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| 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.
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| The binary value expressed on these selector pins determines the selected input pin.
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| A 2-to-1 multiplexer has a [[boolean equation]] where <math>\scriptstyle A</math> and <math>\scriptstyle B</math> are the two inputs, <math>\scriptstyle S</math> is the selector input, and <math>\scriptstyle Z</math> is the output:
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| : <math>Z = ( A \cdot \overline{S}) + (B \cdot S)</math>
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| [[File:Multiplexer 2-to-1.svg|thumb|350px|A 2-to-1 mux]]
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| Which can be expressed as a [[truth table]]:
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| {| class="wikitable"
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| |-
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| |<math>\scriptstyle S</math> || <math>\scriptstyle A</math> || <math>\scriptstyle B</math> || <math>\scriptstyle Z</math>
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| |-
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| |rowspan="4"| 0
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| |rowspan="2"|1 || 1 || 1
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| |-
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| || 0 || 1
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| |-
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| |rowspan="2"|0 || 1 || 0
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| |-
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| || 0 || 0
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| |-
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| |rowspan="4"| 1
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| |rowspan="2"|1 || 1 || 1
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| |-
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| || 0 || 0
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| |-
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| |rowspan="2"|0 || 1 || 1
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| |-
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| || 0 || 0
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| |}
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| This truth table shows that when <math>\scriptstyle S=0</math> then <math>\scriptstyle Z=A</math> but when <math>\scriptstyle S=1</math> then <math>\scriptstyle Z=B</math>. A straightforward realization of this 2-to-1 multiplexer would need 2 AND gates, an OR gate, and a NOT gate.
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| Larger multiplexers are also common and, as stated above, require <math>\scriptstyle \left \lceil \log_2(n) \right \rceil</math> selector pins for <math>n</math> 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.
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| <gallery>
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| File:Multiplexer 4-to-1.svg|4-to-1 mux
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| File:Multiplexer 8-to-1.svg|8-to-1 mux
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| File:Multiplexer 16-to-1.svg|16-to-1 mux
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| </gallery>
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| The boolean equation for a 4-to-1 multiplexer is:
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| :<math>F = (A \cdot \overline{S_0} \cdot \overline{S_1}) + (B \cdot S_0 \cdot \overline {S_1}) + (C \cdot \overline{S_0} \cdot S_1 ) + (D \cdot S_0 \cdot S_1)</math>
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| The following 4-to-1 multiplexer is realized from [[3-state buffers]] and AND gates (the AND gates are acting as the decoder):
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| [[File:Mux from 3 state buffers.png|200px]]
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| Note that the subscripts on the <math>\scriptstyle I_n</math> inputs indicate the decimal value of the binary control inputs at which that input is let through.
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| ===Chaining multiplexers===
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| 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.
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| ===List of ICs which provide multiplexing===
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| The [[7400 series]] has several ICs that contain multiplexer(s):
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| {| class="wikitable"
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| |-
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| ! S.No. !! IC No. !! Function !! Output State
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| | 1
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| | 74157
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| | Quad 2:1 mux.
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| | Output same as input given
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| |-
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| | 2
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| | 74158
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| | Quad 2:1 mux.
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| | Output is inverted input
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| |-
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| | 0
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| | 74153
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| | Dual 4:1 mux.
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| | Output same as input
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| |-
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| | 5
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| | 74352
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| | Dual 4:1 mux.
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| | Output is inverted input
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| |-
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| | 9
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| | 74151A
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| | 16:1 mux.
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| | Both outputs available (i.e., complementary outputs)
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| |-
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| | 6
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| | 74151
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| | 8:1 mux.
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| | Output is inverted input
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| |-
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| | 7
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| | 74150
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| | 16:1 mux.
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| | Output is inverted input
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| |}
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| ==Digital demultiplexers==
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| Demultiplexers take one data input and a number of selection inputs, and they have several outputs.
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| They forward the data input to one of the outputs depending on the values of the selection inputs.
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| Demultiplexers are sometimes convenient for designing general purpose logic, because if the demultiplexer's input is always true, the demultiplexer acts as a [[decoder]].
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| This means that any function of the selection bits can be constructed by logically OR-ing the correct set of outputs.
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| If X is the input and S is the selector, and A and B are the outputs:
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| <math>A = ( X \cdot \overline{S})</math>
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| <math>B = ( X \cdot S)</math>
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| [[File:Demultiplexer Example01.svg|thumb|450px|left|Example: A Single Bit 1-to-4 Line Demultiplexer]]
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| <br clear="all" />
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| ===List of ICs which provide demultiplexing===
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| The [[7400 series]] has several ICs that contain demultiplexer(s):
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| {| class="wikitable"
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| |-
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| ! S.No. !! IC No. (7400) !! IC No. (4000) !! Function !! Output State
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| |-
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| | 1
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| | 74139
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| | Dual 1:4 demux.
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| | Output is inverted input
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| |-
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| | 3
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| | 74156
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| | Dual 1:4 demux.
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| | Output is [[open collector]]
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| |-
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| | 4
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| | 74138
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| | 1:8 demux.
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| | Output is inverted input
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| |-
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| | 5
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| | 74238
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| | 1:8 demux.
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| |-
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| | 6
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| | 74154
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| | 1:16 demux.
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| | Output is inverted input
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| |-
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| | 7
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| | 74159
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| | CD4514/15
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| | 1:16 demux.
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| | Output is open collector and same as input
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| |}
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| ==Multiplexers as PLDs==
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| Multiplexers can also be used as components of [[programmable logic device]]s. By specifying the logic arrangement in the input signals, a custom logic circuit can be created. The selector inputs then act as the logic inputs. This is especially useful in situations when cost is a factor and for modularity.
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| ==See also==
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| {{Wiktionary|multiplexer|demultiplexer}}
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| * [[Priority encoder]]
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| * [[Inverse multiplexer]]
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| * [[Statistical multiplexer]]
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| * [[Digital subscriber line access multiplexer]] (DSLAM)
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| * [[Rule 184]], a [[cellular automaton]] in which each cell acts as a multiplexer for the values from the two adjacent cells
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| * [[Multiplexing]]
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| ** [[CDMA|Code-division multiplexing]]
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| ** [[Frequency-division multiplexing]]
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| ** [[Time-division multiplexing]]
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| **[[Wavelength-division multiplexing]]
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| **[[Statistical multiplexing]]
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| ==References==
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| {{Reflist}}
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| ==Further reading==
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| *{{cite book
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| |author1=M. Morris Mano
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| |author2=Charles R. Kime
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| |title=Logic and Computer Design Fundamentals
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| |edition=4
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| |isbn=0-13-198926-X
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| |publisher=[[Prentice Hall]]
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| |year=2008
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| }}
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| {{commons category|Multiplexers}}
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| {{CPU technologies}}
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| [[Category:Multiplexing]]
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| [[Category:Digital circuits]]
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