A multiplexer is a combinational circuit that has many data inputs and a single output, depending on control or select inputs. For N input lines, log2(N) selection lines are required, or equivalently, for 2^n input lines, n selection lines are needed. Multiplexers are also known as “N-to-1 selectors,” parallel-to-serial converters, many-to-one circuits, and universal logic circuits. They are mainly used to increase the amount of data that can be sent over a network within a certain amount of time and bandwidth.
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Now the implementation of 4:1 Multiplexer using truth table and gates.Â
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Multiplexer can act as universal combinational circuit. All the standard logic gates can be implemented with multiplexers.Â
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a) Implementation of NOT gate using 2 : 1 Mux
NOT Gate :Â
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We can analyze itÂ
Y = x’.1 + x.0 = x’Â
It is NOT Gate using 2:1 MUX.Â
The implementation of NOT gate is done using “n” selection lines. It cannot be implemented using “n-1” selection lines. Only NOT gate cannot be implemented using “n-1” selection lines.Â
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b) Implementation of AND gate using 2 : 1 Mux
AND GATEÂ
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This implementation is done using “n-1” selection lines.Â
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c) Implementation of OR gate using 2 : 1 Mux using “n-1” selection lines.
OR GATEÂ
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Implementation of NAND, NOR, XOR and XNOR gates requires two 2:1 Mux. First multiplexer will act as NOT gate which will provide complemented input to the second multiplexer.Â
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d) Implementation of NAND gate using 2 : 1 Mux
NAND GATEÂ
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e) Implementation of NOR gate using 2 : 1 Mux
NOR GATEÂ
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f) Implementation of EX-OR gate using 2 : 1 Mux
EX-OR GATEÂ
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g) Implementation of EX-NOR gate using 2 : 1 Mux
EX-NOR GATEÂ
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Implementation of Higher order MUX using lower order MUXÂ
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a) 4 : 1 MUX using 2 : 1 MUX
Three(3) ???? : 1 MUX are required to implement 4 : 1 MUX.Â
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Similarly,Â
While 8 : 1 MUX require seven(7) ???? : 1 MUX, 16 : 1 MUX require fifteen(15) ???? :1 MUX, 64 : 1 MUX requires sixty three(63)​ 2 : 1 MUX.Â
Hence, we can draw a conclusion,Â
2n : 1 MUX requires (2^n – 1) 2 : 1 MUX.Â
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b) 16 : 1 MUX using 4 : 1 MUX
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In general, to implement B : 1 MUX using A : 1 MUX , one formula is used to implement the same.Â
B / A = K1,Â
K1/ A = K2,Â
K2/ A = K3Â
………………Â
KN-1 / A = KN = 1 (till we obtain 1 count of MUX).Â
And then add all the numbers of MUXes = K1 + K2 + K3 + …. + KN.Â
For example​ : To implement 64 : 1 MUX using 4 : 1 MUXÂ
Using the above formula, we can obtain the same.Â
64 / 4 = 16Â
16 / 4 = 4Â
4 / 4 = 1 (till we obtain 1 count of MUX)Â
Hence, total number of 4 : 1 MUX are required to implement 64 : 1 MUX = 16 + 4 + 1 = 21.Â
An example to implement a boolean function if minimal and don’t care terms are given using MUX​.Â
f ( A, B, C) = ? ( 1, 2, 3, 5, 6 ) with don’t care (7) using 4 : 1 MUX using asÂ
a) AB as select : ????xpanding the minterms to its boolean form and will see its 0 or 1 value in Cth place so that they can be placed in that manner.Â
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b) AC as select : Expanding the minterms to its boolean form and will see its 0 or 1 value in Bth place so that they can be place in that manner.Â
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c) BC as select : ????xpanding the minterms to its boolean form and will see its 0 or 1 value in Ath place so that they can be place in that manner.Â
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Advantages and disadvantages of Multiplexers in Digital Logic:
 Advantages of Multiplexers in Digital Logic:
1.Space-saving: Multiplexers consider numerous signs to be directed through a solitary channel, which recoveries space in computerized circuits.
2.Cost-successful: Multiplexers can assist with decreasing the expense of Advanced circuits by diminishing the quantity of parts required.
3.Time-saving: Multiplexers can save time in computerized circuits by decreasing the quantity of parts that should be wired together, subsequently diminishing the intricacy of the circuit.
4.Flexibility: Multiplexers are profoundly adaptable and can be utilized in a great many applications
 Disadvantages of Multiplexers in Digital Logic:
1.Limited number of data sources: The quantity of sources of info that can be taken care of by a multiplexer is restricted by the quantity of control lines, which can be a disservice in certain applications.
2.Delay: Multiplexers can present some postpone in the sign way, which can influence the exhibition of the circuit.
3.Complex control rationale: The control rationale for multiplexers can be perplexing, particularly for bigger multiplexers with an enormous number of data sources.
4.Power utilization: Multiplexers can consume more power contrasted with other straightforward rationale entryways, particularly when they have countless data sources.
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Last Updated :
20 Mar, 2024
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