Digital Electronics - Multiplexers

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A digital logic circuit that accepts several data inputs and allows only one of them at a time to flow through the output is called a multiplexer or MUX. This article is meant for explaining multiplexer in digital electronics, its block diagram, function, and different types. So, let us start with the basic introduction of multiplexer

What is a Multiplexer?

As already mentioned, a multiplexer, also referred to as MUX, is a combination logic circuit that is designed to accept multiple input signals and transfer only one of them through the output line. In simple words, a multiplexer is a digital logic device that selects one-out-of-N (N = 2ⁿ) input data sources and transmits the selected data to a single output line.

The multiplexer is also called data selector as it selects one from several. The block diagram of a typical 2ⁿ:1 multiplexer is shown in Figure 1.

In the case of multiplexer, the selection of desired data input to flow through the output line is controlled with the help of SELECT lines. In the block diagram of mux in Figure 1, I₀, I₁,... I_n-1, i.e., (2ⁿ) are the input lines, and "n" be the select lines. These select lines will determine which input is to be routed to the output.

Hence, the multiplexer works as a multi-position switch whose operation is controlled by digital signals. These digital control signals are applied to the select lines to determine which data input will be switched to the output line.

Function of Multiplexer

Multiplexer is a digital logic device which is used to perform multiplexing of data. Where, multiplexing simply means sharing of data. Technically, when a particular data is selected from multiple input data sources and transmitted the selected data to a single output channel, it is called multiplexing.

There are two types of multiplexing namely, frequency multiplexing and time multiplexing.

When multiple devices are connected to a single transmission line in a system. At any point of time, only one device is using the line to transmit data, then this is called time multiplexing. On the other hand, when multiple devices share a common line to transmit data but at different frequencies, it is called frequency multiplexing.

Types of Multiplexers

Based on input data lines and select lines, the multiplexer can be of several types. But, in this article, we will discuss only the following three types of multiplexers −

• 2×1 Multiplexer
• 4×1 Multiplexer

Let us discuss each of these three multiplexers individually.

2×1 Multiplexer

The block diagram of a 2×1 multiplexer is shown in Figure 2. The 2×1 multiplexer is basic two input multiplexer which has two data input lines designated as I₀ and I₁, one data select line denoted by S and one output line denoted by Y. The 2×1 mux is used to connect two 1-bit data sources to a common designation.

In the 2×1 multiplexer, the logic level of the digital signal applied to the select line S determines which data input will pass through the output line. The operation of the 2×1 multiplexer can be understood from the following truth table.

4×1 Multiplexer

4×1 Multiplexer has four data inputs I₃, I₂, I₁ & I₀, two selection lines s₁ & s₀ and one output Y. The block diagram of 4×1 Multiplexer is shown in the following figure.

One of these 4 inputs will be connected to the output based on the combination of inputs present at these two selection lines. Truth table of 4×1 Multiplexer is shown below.

From Truth table, we can directly write the Boolean function for output, Y as

$$\mathrm{Y\:=\:{S_{1}}'{S_{0}}'I_{0}\:+\:{S_{1}}'S_{0}I_{1}\:+\:S_{1}{S_{0}}'I_{2}\:+\:S_{1}S_{0}I_{3}}$$

We can implement this Boolean function using Inverters, AND gates & OR gate. The circuit diagram of 4×1 multiplexer is shown in the following figure.

We can easily understand the operation of the above circuit. Similarly, you can implement 8×1 Multiplexer and 16×1 multiplexer by following the same procedure.

Implementation of Higher-order Multiplexers

Now, let us implement the following two higher-order Multiplexers using lower-order Multiplexers.

• 8×1 Multiplexer
• 16×1 Multiplexer

8×1 Multiplexer

In this section, let us implement 8×1 Multiplexer using 4×1 Multiplexers and 2×1 Multiplexer. We know that 4×1 Multiplexer has 4 data inputs, 2 selection lines and one output. Whereas, 8×1 Multiplexer has 8 data inputs, 3 selection lines and one output.

So, we require two 4×1 Multiplexers in first stage in order to get the 8 data inputs. Since, each 4×1 Multiplexer produces one output, we require a 2×1 Multiplexer in second stage by considering the outputs of first stage as inputs and to produce the final output.

Let the 8×1 Multiplexer has eight data inputs I₇ to I₀, three selection lines s₂, s₁ & s0 and one output Y. The Truth table of 8×1 Multiplexer is shown below.

We can implement 8×1 Multiplexer using lower order Multiplexers easily by considering the above Truth table. The block diagram of 8×1 Multiplexer is shown in the following figure.

The same selection lines, s₁ & s₀ are applied to both 4×1 Multiplexers. The data inputs of upper 4×1 Multiplexer are I₇ to I₄ and the data inputs of lower 4×1 Multiplexer are I₃ to I₀. Therefore, each 4×1 Multiplexer produces an output based on the values of selection lines, s₁ & s₀.

The outputs of first stage 4×1 Multiplexers are applied as inputs of 2×1 Multiplexer that is present in second stage. The other selection line, s₂ is applied to 2×1 Multiplexer.

• If s₂ is zero, then the output of 2×1 Multiplexer will be one of the 4 inputs I₃ to I₀ based on the values of selection lines s₁ & s₀.

• If s₂ is one, then the output of 2×1 Multiplexer will be one of the 4 inputs I₇ to I₄ based on the values of selection lines s₁ & s₀.

Therefore, the overall combination of two 4×1 Multiplexers and one 2×1 Multiplexer performs as one 8×1 Multiplexer.

16×1 Multiplexer

In this section, let us implement 16×1 Multiplexer using 8×1 Multiplexers and 2×1 Multiplexer. We know that 8×1 Multiplexer has 8 data inputs, 3 selection lines and one output. Whereas, 16×1 Multiplexer has 16 data inputs, 4 selection lines and one output.

So, we require two 8×1 Multiplexers in first stage in order to get the 16 data inputs. Since, each 8×1 Multiplexer produces one output, we require a 2×1 Multiplexer in second stage by considering the outputs of first stage as inputs and to produce the final output.

Let the 16×1 Multiplexer has sixteen data inputs I₁₅ to I₀, four selection lines s₃ to s₀ and one output Y. The Truth table of 16×1 Multiplexer is shown below.

We can implement 16×1 Multiplexer using lower order Multiplexers easily by considering the above Truth table. The block diagram of 16×1 Multiplexer is shown in the following figure.

The same selection lines, s₂, s₁ & s₀ are applied to both 8×1 Multiplexers. The data inputs of upper 8×1 Multiplexer are I₁₅ to I₈ and the data inputs of lower 8×1 Multiplexer are I₇ to I₀. Therefore, each 8×1 Multiplexer produces an output based on the values of selection lines, s₂, s₁ & s₀.

The outputs of first stage 8×1 Multiplexers are applied as inputs of 2×1 Multiplexer that is present in second stage. The other selection line, s₃ is applied to 2×1 Multiplexer.

If s₃ is zero, then the output of 2×1 Multiplexer will be one of the 8 inputs Is₇ to I₀ based on the values of selection lines s₂, s₁ & s₀.

If s₃ is one, then the output of 2×1 Multiplexer will be one of the 8 inputs I₁₅ to I₈ based on the values of selection lines s₂, s₁ & s₀.

Therefore, the overall combination of two 8×1 Multiplexers and one 2×1 Multiplexer performs as one 16×1 Multiplexer.

Applications of Multiplexers

In digital electronics, multiplexers have numerous applications in almost all types of digital systems. Some important applications of multiplexers are as follows −

• Data routing and data selection
• Parallel to series conversion
• Logic function implementation
• Generation of waveform, etc.

Conclusion

In this tutorial, we discussed in detail the different types of multiplexers used in digital electronics along with their functions and applications.