Multiplexer in Digital Electronics

In this lecture, we are going to cover another combinational circuit called Multiplexer in Digital Electronics. We will cover what is Multiplexer, the block diagram of the multiplexer, the types of multiplexer, the need of multiplexers, and the advantages of multiplexer and in the end, we will see the application of multiplexer.

What is Multiplexer

A Multiplexer, also known as a MUX, is a special type of combinational circuit used in digital electronics. The block diagram of an n-to-1 multiplexer and its equivalent circuit is shown in the figure below

As shown in the figure, there are n-data inputs, one output, and a m select inputs, with 2^m = n

A multiplexer is a digital circuit that selects one of the n data inputs and routes it to the output. The selection of one of the n inputs is done by the select lines.

To select n inputs we need m select lines such that 2^m = n. Depending on the digital code applied at the select inputs, one out of n data sources is selected and transmitted to the single output Y.

The operation of a Multiplexer is controlled by the select inputs. By applying a particular digital code to the select inputs, one out of n data sources is selected and transmitted to the output. In other words, it acts like a digitally controlled single pole, multiple-way switch. At any given moment, the output is connected to only one of the n data inputs.

The Multiplexer also includes an enable input (E) which is typically active low. This input, when activated, allows the Multiplexer to perform its selected operation.

Multiplexers find widespread use in digital circuits. Some common applications include data routing, data selection, data transmission, and signal processing. They offer advantages such as compactness, simplified circuit design, and enhanced flexibility in data manipulation.

Overall, Multiplexers play a crucial role in optimizing digital circuits by efficiently selecting and routing data to the desired destination.

Also Read: Magnitude Comparator and Digital Comparator

Need of Multiplexer

• In most electronic systems, digital data is available on more than one line. It is necessary to route this data over a single line.

• Under such circumstances, we require a circuit that selects one of the many inputs at a time.

• This circuit is nothing else but a multiplexer, which has many inputs, one output, and some select inputs.

• Multiplexer improves the reliability of the digital system because it reduces the number of external wired connections.

Types of Multiplexer

There are several types of multiplexer in digital electronics, each with a different number of data inputs and select inputs. Here is a brief description of the main types:

Type	Description
2 to 1 Multiplexer	A 2 to 1 multiplexer has two data inputs, one select input, and one output. It selects one of the two data inputs based on the selected input.
4 to 1 Multiplexer	A 4 to 1 multiplexer has four data inputs, two select inputs, and one output. It selects one of the four data inputs based on the selected inputs.
8 to 1 Multiplexer	An 8 to 1 multiplexer has eight data inputs, three select inputs, and one output. It selects one of the eight data inputs based on the selected inputs.
16 to 1 Multiplexer	A 16 to 1 multiplexer has sixteen data inputs, four select inputs, and one output. It selects one of the sixteen data inputs based on the selected inputs.
n-to-1 Multiplexer	An n to 1 multiplexer has n data inputs, log2(n) select inputs, and one output. It selects one of the n data inputs based on the selected inputs.

now we are going to learn about each type of multiplexer in detail.

Also Read: BCD Adder – Block Diagram, Truth table & Circuit

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2 To 1 Multiplexer

The block diagram of 2 to 1 Multiplexer is shown in the below figure. it has two data inputs D0 and D1, one select input S, an enable input, and one output.

2 to 1 Multiplexer Truth Table

• The truth table of 2 to 1 Multiplexer is shown in the figure below.

Realization of 2 To 1 Multiplexer using Gates

• Write a more elaborate truth table of 2 to 1 Multiplexer as shown in the figure below.

From the above truth table, it is clear that Y =1 for only two conditions shown by the shaded boxes.

\therefore \mathbf{Y = E \bar SD_0 + ESD_1}

\therefore \mathbf{Y = E (\bar SD_0 + SD_1)}

• 2 to 1 multiplexer circuit diagram is shown in the figure below:

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4 To 1 Multiplexer

• The below figure shows the block diagram of a 4 to 1 multiplexer.

• The truth table of 4 to 1 multiplexer is shown in the below figure.

• Note that n = 4 hence a number of select lines i.e. m =2 so that 2^m = n.

• The truth table tells us that if S₁S₀ = 00, the data bit D₀ is selected and routed to output.

Y = D₀ … when S₁S₀ = 00

• Similarly, if S₁S₀ = 01, then D₁ is selected and routed to the output.

Y = D₁ … when S₁S₀ = 01

• Y = D₂ for S₁S₀ = 10 and Y = D₃ … when S₁S₀ = 11

• The output will be high when the selected input (D0, D1, etc.) is 1. Hence the logical expression for output in the SOP form is as follows.

\mathbf{Y = \bar S_1 \bar S_0D_0 + \bar S_1 S_0 D_1 + S_1 \bar S_0 D_2 + S_1S_0D_3 }

• This expression can be realized using basic gates as shown in the figure below.

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8 to 1 Multiplexer

• The block diagram of an 8 to 1 multiplexer is shown in the figure.

• The 8 to 1 multiplexer truth table is shown in the figure below.

• When the enable input is 0, the output will be 0 irrespective of any input.

• With E = 1, we can select any one of the eight data inputs and connect it to the output.

• For example if S₂ S₁ S₀ = 0 1 1 then the data input D₃ is selected and output Y will follow the input D₃.

The expression for output Y can be obtained from the truth table of the figure shown.

The 8 to 1 multiplexer circuit diagram is shown in the figure below.

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16 to 1 Multiplexer

• The block diagram of a 16 to 1 Multiplexer is shown in the figure below. it has 16 data inputs, 4 select lines, one enable input, and one output.

• When the enable input E = 0, the multiplexer output Y = 0 irrespective of the status of other inputs.

• With E = 1, we can select any one of the 16 inputs with the help of select input lines and connect the selected input to the output.

• The 16 to 1 multiplexer truth table is shown in the figure below.

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Advantages Of Multiplexer

• It reduces the number of wires, so it reduces the circuit complexity and cost.
• We can implement many combinational circuits using Multiplexer.
• It simplifies the logic design.
• It does not need the k-maps and simplification.

Application Of Multiplexer

Some of the important applications of a multiplexer area as follows:

1. It is used as a data selector to select one out of many data inputs.
2. It is used for simplification of logic design.
3. In the data acquisition system.
4. In designing the combinational circuits.
5. In the digital-to-analog converter.
6. To minimize the number of connections.

FAQs

Also Read:

• Half Adder in Digital Electronics
• Full Adder in Digital Electronics
• Half Subtractor in Digital Electronics
• Full Subtractor in Digital Electronics