Multiplexers in Digital Logic

In this article we will go through the multiplexer, we will first define what is a multiplexer then we will go through its types which are 2×1 and 4×1, then we will go through the Implementation of the 2×1 mux and higher mux with lower order mux, At last we will conclude our article with some applications, advantages and some FAQs.

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 [Tex]2^n[/Tex] 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.

The Mux can be of different types based on input but in this article we will go through two major types of mux which are

• 2×1 Mux
• 4×1 Mux
  

The 2×1 is a fundamental circuit which is also known 2-to-1 multiplexer that are used to choose one signal from two inputs and transmits it to the output. The 2×1 mux has two input lines, one output line, and a single selection line. It has various applications in digital systems such as in microprocessor it is used to select between two different data sources or between two different instructions.

Block Diagram of 2:1 Multiplexer with Truth Table

Given Below is the Block Diagram and Truth Table of 2:1 Mux. In this Block Diagram where I0 and I1 are the input lines ,Y is the output line and S0 is a single select line.

The output of the 2×1 Mux will depend on the selection line S0,

• When S is 0(low), the I0 is selected
• when S0 is 1(High), I1 is selected

Logical Expression of 2×1 Mux

Using the Truth Table ,the Logical Expression for Mux can be determined as

[Tex]Y=\overline{S_0}.I_0+S_0.I_1[/Tex]

Circuit Diagram of 2×1 Multiplexers

Using truth table the circuit diagram can be given as

The 4×1 Multiplexer which is also known as the 4-to-1 multiplexer. It is a multiplexer that has 4 inputs and a single output. The Output is selected as one of the 4 inputs which is based on the selection inputs. The number of the Selection lines will depend on the number of the input which is determined by the equation [Tex]log_2n[/Tex],In 4×1 Mux the selection lines can be determined as [Tex]log_4=2[/Tex],slo two selections are needed.

Block Diagram of 4×1 Multiplexer

In the Given Block Diagram I0, I1, I2, and I3 are the 4 inputs and Y is the Single output which is based on Select lines S0 and S1.

The output of the multiplexer is determined by the binary value of the selection lines

• When S1S0=00, the input I0 is selected.
• When S1S0=01, the input I1 is selected.
• When S1S0=10, the input I2 is selected.
• When S1S0=11, the input I3 is selected.

Truth Table of 4×1 Multiplexer

Given Below is the Truth Table of 4×1 Multiplexer

Circuit Diagram of 4×1 Multiplexers

Using truth table the circuit diagram can be given as
 

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

Given below are the Implementation of Different gate using 2:1 Mux

Implementation of NOT gate using 2 : 1 Mux

The Not gate from 2:1 Mux can be obtained by

• Connect the input signal to one of the data input lines(I0).
• Then connect a line (0 or 1) to the other data input line(I1)
• Connect the same input line Select line S0 which is connected to D0.

Given Below is the Diagram for the Logical Representation of NOT gate using 2 : 1 Mux

Implementation of AND gate using 2 : 1 Mux

The And gate from 2:1 Mux can be obtained by

• Connect the input Y to I1.
• Connect the input X to the selection line S0.
• Connect a line(0) to I0.

Given Below is the Diagram for the Logical Representation of AND gate using 2 : 1 Mux
 

For further more on the Implementation of AND gate using 2 : 1 Mux
 

Implementation of OR gate using 2 : 1 Mux

The OR gate from 2:1 Mux can be obtained by  

• Connect input X to the selection line S0.
• Connect input Y to I1.
• Connect Line(1) to I1.

Given Below is the Diagram for the Logical Representation of OR gate using 2 : 1 Mux

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. 
 

Implementation of NAND gate using 2 : 1 Mux

The NAND gate from 2:1 Mux can be obtained by  

• In first mux take inputs and 1 and 0 and y as selection line.
• In Second MUX the Output from mux is connected to I1.
• line(1) is given to the I0.
• x is given as selection line for the second Mux.

Given Below is the Diagram for the Logical Representation of NAND gate using 2 : 1 Mux
 

For further more on the Implementation of NAND gate using 2 : 1 Mux

 

Implementation of NOR gate using 2 : 1 Mux

The Nor gate from 2:1 Mux can be obtained by  

• In first mux take inputs and 1 and 0 and y as selection line.
• In Second MUX the Output from mux is connected to I0.
• line(0) is given to the I1.
• x is given as selection line for the second Mux.

Given Below is the Diagram for the Logical Representation of NOR gate using 2 : 1 Mux
 

For further more on the Implementation of NOR gate using 2 : 1 Mux

Implementation of EX-OR gate using 2 : 1 Mux

The Nor gate from 2:1 Mux can be obtained by  

• In first mux take inputs and 1 and 0 and y as selection line.
• In Second MUX the Output from mux is connected to I1.
• y is given to the I0.
• x is given as selection line for the second Mux.

Given Below is the Diagram for the Logical Representation of EX-OR gate using 2 : 1 Mux
 

Implementation of EX-NOR gate using 2 : 1 Mux

Given Below is the Diagram for the Logical Representation of EX-OR gate using 2 : 1 Mux

The Nor gate from 2:1 Mux can be obtained by  

• In first mux take inputs and 1 and 0 and y as selection line.
• In Second MUX the Output from mux is connected to I0.
• y is given to the I1.
• x is given as selection line for the second Mux.

Given Below are the Implementation of Higher Order MUX Using Lower Order MUX

4 : 1 MUX using 2 : 1 MUX

Three 2: 1 MUX are required to implement 4 : 1 MUX. 
 

Similarly, 

While an 8:1 MUX requires seven (7) 2:1 MUXes, a 16:1 MUX requires fifteen (15) 2:1 MUXes, and a 64:1 MUX requires sixty-three (63) 2:1 MUXes. Hence, we can draw the conclusion that an [Tex]2^n:1[/Tex] MUX requires [Tex](2^n-1) 2:1 MUXes[/Tex].
 

16 : 1 MUX using 4 : 1 MUX 

Given Below is the logical Diagram of 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 

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

And then add all the numbers of MUXes = K1 + K2 + K3 + …. + K_N. 
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. 

f ( A, B, C) = [Tex]\sum[/Tex] ( 1, 2, 3, 5, 6 ) with don’t care (7)

using A and B as the select lines for 4 : 1 MUX,

AB as select: Expanding 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.
 

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. 


 

BC as select : Expanding the minterms to its boolean form and will see its 0 or 1 value in A^th place so that they can be place in that manner. 


 

Given below are the Advantages and Disadvantages of MUX

Advantages of MUX

Given below are the Advantages of MUX

• Efficiency: The Mux has good efficiency in routing multiple input signals to a single out signal based on control signals.
• Optimization: The Mux helps to conserve resources such as wires, pins and integrated circuit(IC).
• Different Implementation: The Mux can be used to implement different digital logic functions such AND,OR etc.
• Flexibility: Mux can be easily configure according to the requirements and accommodate different data sources, enhancing system versatility.

Disadvantages of MUX

Given Below are the Disadvantages of MUX

• Limited number of data sources: The number of input that can be taken by a multiplexer is restricted by the number of control lines, which can cause limitations in certain applications.
• Delay: Multiplexers can have some delay in the signal path, which can have impact on the performance of the circuit.
• Complex control rationale: The control logic for multiplexers can be complex, particularly for bigger multiplexers with an large number of inputs.
• Power utilization: Multiplexers can consume more power compared with other simple logic gate, particularly when they have a large number of inputs.

Given Below are the Applications of MUX

• Data Routing: The Mux is used for data routing in the digital system where they select one of the several data lines and re-route it the output.
• Data Selection: The Mux is used for data selection where they select data source according to the select lines.
• Analog-to-Digital Conversion: The Mux are used in ADC to select different analog input channels.
• Address Decoding: The Mux are used in Microprocessors or memory for address decoding.
• Logic Function Implementation: Muxes can be used to implement various logic functions.

In this Article we have gone through the MUX, we have seen Different Types of Mux which are 2×1 and 4×1 Mux, we have gone through the implementation of the 2×1 mux and higher mux with lower order mux. Also we have gone through its Advantages, Disadvantages and Applications in brief.

Why is the control logic for multiplexers is considered complex?

The Mux can be complex especially for larger multiplexers because of the control signals which select inputs based on the application requirements.

What are the different types of multiplexer architectures?

Mux architectures are changed on factors such as the total number of inputs, the number of select lines and the logic used for input selection.

How do multiplexers are used digital signal processing (DSP) applications?

In DSP applications, multiplexers are used for signal routing, selection, and processing.