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Multiplexers in Digital Logic

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It is a combinational circuit which have many data inputs and single output depending on control or select inputs.&#x200b For N input lines, log n (base2) selection lines, or we can say that for 2n input lines, n selection lines are required. Multiplexers are also known as ?ta n selector, parallel to serial convertor, many to one circuit, universal logic circuit&#x200b&#x201d. Multiplexers are mainly used to increase amount of the data that can be sent over the network within certain amount of time and bandwidth. 


 




Now the implementation of 4:1 Multiplexer using truth table and gates. 

 



 




Multiplexer can act as universal combinational circuit. All the standard logic gates can be implemented with multiplexers. 

 

a) Implementation of NOT gate using 2 : 1 Mux


NOT Gate : 

 




We can analyze it 
Y = x’.1 + x.0 = x’ 
It is NOT Gate using 2:1 MUX. 
The implementation of NOT gate is done using &#x201cn&#x201d selection lines. It cannot be implemented using &#x201cn-1&#x201d selection lines. Only NOT gate cannot be implemented using &#x201cn-1&#x201d selection lines. 

  
 

b) Implementation of AND gate using 2 : 1 Mux


AND GATE 

 





This implementation is done using &#x201cn-1&#x201d selection lines. 

  
 

c) Implementation of OR gate using 2 : 1 Mux using &#x201cn-1&#x201d selection lines.


OR GATE 

 




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. 
 

d) Implementation of NAND gate using 2 : 1 Mux


NAND GATE 

 




 

e) Implementation of NOR gate using 2 : 1 Mux


NOR GATE 

 





 

f) Implementation of EX-OR gate using 2 : 1 Mux


EX-OR GATE 

 




 

g) Implementation of EX-NOR gate using 2 : 1 Mux


EX-NOR GATE 

 




Implementation of Higher order MUX using lower order MUX 
 

a) 4 : 1 MUX using 2 : 1 MUX


Three(3) ???? : 1 MUX are required to implement 4 : 1 MUX. 


 

I1 and I2 in the outputs should be replaced




Similarly, 

While 8 : 1 MUX require seven(7) ???? : 1 MUX, 16 : 1 MUX require fifteen(15) ???? :1 MUX, 64 : 1 MUX requires sixty three(63)&#x200b 2 : 1 MUX. 
Hence, we can draw a conclusion, 
2n : 1 MUX requires (2^n – 1) 2 : 1 MUX. 
 

b) 16 : 1 MUX using 4 : 1 MUX




 




In general, to implement B : 1 MUX using A : 1 MUX , one formula is used to implement the same. 
B / A = K1, 
K1/ A = K2, 
K2/ A = K3 

……………… 

KN-1 / A = KN = 1 (till we obtain 1 count of MUX). 

And then add all the numbers of MUXes = K1 + K2 + K3 + …. + KN
For example&#x200b : To implement 64 : 1 MUX using 4 : 1 MUX 
Using the above formula, we can obtain the same. 
64 / 4 = 16 
16 / 4 = 4 
4 / 4 = 1 (till we obtain 1 count of MUX) 
Hence, total number of 4 : 1 MUX are required to implement 64 : 1 MUX = 16 + 4 + 1 = 21. 


An example to implement a boolean function if minimal and don’t care terms are given using MUX&#x200b. 
f ( A, B, C) = ? ( 1, 2, 3, 5, 6 ) with don&#x2019t care (7) using 4 : 1 MUX using as 
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. 


 





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. 


 




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. 


 



 

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.




 



Last Updated : 19 Sep, 2023
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