Circuit

# What is Multiplexer and How Do They Work? – Circuit of 2 to 1, 4 to 1, 8 to 1 MUX In this tutorial, we will learn about an interesting topic in digital or communication called multiplexer, it is digital circuit using combination circuit called multiplexer. We learn different type of multiplexer like 2 to 1, 4 to1, 8 to 1, 16 to 1 and 32 to 1 multiplexer, some of the important uses of multiplexer.

The multiplexer is a combinational logic circuit that designed to switch one of several input lines to a single common output line. It is a fast rotary switch connecting multiple input lines. In short form it is written by MUX

Multiplexer can be either design by digital circuit and analog circuit. In digital, it is made from high speed logic gate to switch binary data. In analog, it can be made by using transistor, MOSFET’s or relay switch to switch one of the voltage or current input transmit to a single output.

## What is Multiplexing?

Multiplexing is a process in which one or more signal input and transmitting on a single output. In communication system the channel is a scarce quantity and must be properly use it. The concept of multiplexing is very useful for cost effective and efficient utilization of channel. It allows multiple users on a single channel.

Three common types of Multiplexing;

• Time
• Frequency
• Space

Two are best examples of Multiplexing Systems used in our daily life in landline telephone network and Cable TV. Multiplexer are use in both for analog and digital signal.

A basic multiplexer have various input and single output line. It is found many digital applications. These are data selection, digital counters, waveform generators, logic function generators, communication systems, telephone network, etc. we are going to discuss various types of multiplexers and its design.

The MUX is a digital switching circuit, also known as data selector. It has several inputs and single output line the selection of single input line is depending on the set of select line, for particular input line routed on the single output line.

The basic information of multiplexing is shown in figure. In which several input source are routed to single output when select line is enable. The block diagram of multiplexer has “n” input line and “m” selection line and single output line. If “m” selection line, than the number of possible input line is n (2m  = n)

This type of multiplexer is 2n × 1 multiplexer or 2n-to-1 multiplexer. For example, if the number of input lines is 4, then 2 select lines are required. Similarly, to select one of 8 input lines, 3 select lines are required. Mostly used multiplexers are 2-to-1, 4-to-1, 8-to-1 and 16-to-1 multiplexers. Multiplexers are also available in IC forms. ICs number of multiplexer are 74157 (2-to-1 MUX), 78158 (2-to-1 MUX), 74153 (4-to-1 MUX), 74152 (8-to-1 MUX) and 74150 (16-to-1 MUX).

## Multiplexer circuit

It is much type like 2-to-1, 4-to-1, and 8-to-1 multiplexers. Each MUX have different circuits, Boolean expression, truth table and working principle. Now we are going to discuss each type of multiplexer one by one.

### 2 to 1 Multiplexer

#### 2 to 1 Multiplexer Circuit

2 to 1 multiplexer is the digital multiplexer logic circuit in which two data inputs lines D0 and D1 and one selects line S and one output line Y. The requirement for implementation of a 2-to-1 multiplexer circuit 2 AND gates, an OR gate, and a NOT gate. The logic symbol, block diagram and switching circuit analogy of 2-to-1 multiplexer figure are shown below. A 2-to-1 MUX Logic Symbol Switching Analogy

Input D0 is an applied input to one of the AND gate and D1 is an applied input to the other AND gate. Select line input S is applied to second AND logic gate as a another input and inverted input applied to the first AND logic gate as a second input. The output of these two gates applied to the OR logic gate input.

#### 2 to 1 Multiplexer Working Principle

Initially the input D0 and D1 is high “1”. When select input S=0 is applied to the second AND gate and inverted of S that is 1 applied to the first input of AND gate. Now we know the function of AND gate, if any input is zero the output will be zero. So the second AND gate input is zero. The first AND gate, the invert input S=1 and D1=1 is applied to the AND gate the output is 1. OR logic gate output is “1”.

When select input S=1 is applied to the second AND gate and inverted of S that is 0 applied to the first input of AND gate. Now we know the function of AND gate, if any input is zero the output will be zero. So the first AND gate input is zero. The second AND gate, the invert input S=0 and D1=1 is applied to the AND gate the output is 1. OR logic gate output is “1”.

#### 2 to 1 Multiplexer Truth Table

Truth table of the 2-to-1 multiplexer.

 Select input S Data Input Data Input Output Y 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1

Here, the 2-to-1 multiplexer only connects one of two 1-bit sources to a common output, hence it a 2-to-1 multiplexer.

#### 2 to 1 Multiplexer Boolean Expression

We can write the Boolean expression from the truth table, for the output of the 2-to-1 multiplexer.

Q = S’.D0.D1 + S’.D0.D1‘+ S.D0’.D1 + S.D0.D1
Q = S’.D0 (D1 + D1‘) + S.D1 (D0 + D1‘)
Q = S’.D1 +S.D0      [as per complement law (OR law) i.e. A+A’=1]

In simple

 S Y 0 D0 1 D1

The table shows when select input S=0 them the output will be Y=D0 and when S=1 then Y=D1. We can increase number of data input lines to be selected further. We can use 2-to-1 multiplexer circuit for implement of larger multiplexer circuits.

We can also implement the 2-to-1 multiplexer circuit by using NAND gate. NOR and NAND logic gate are universal gate. Using these universal gates we can implement any digital circuits.

### 4 to 1 Multiplexer

#### 4 to 1 Multiplexer Circuit Diagram

A 4-to-1 multiplexer is a combination digital logic multiplexer circuit. It has four data input lines, two select lines and one output line. For implementation of 4-to-1 MUX logic circuit we need 4 AND gates, an OR gate, and a 2 NOT gate.

In 4-to-1 multiplexer the four input lines D0, D1, D2, and D3, two select lines S0 and S1 as 4-inputs represent. 2m =22 =2 “m” represent the data select line which is 2 and “22=4” 4 is the number of inputs lines will be connected to the four AND gates and the output of four and gates are connected to the OR gates.

The logic symbol, switching circuit analogy and block diagram of 4-to-1 multiplexer figure shown below. 4-to-1 MUX Logic Circuit Logic Symbol Switching Analogy

#### 4 to 1 Multiplexer Working Principle

When both the select inputs S0 = 0, S1 = 0, the top of AND logic gate is enable and other two AND gate is disable, so the data input D0 input line is selected and transmitted as output. Hence, the output Y = D0.

When both the select inputs S0 = 1, S1 = 1, the bottom of AND logic gate is enable and other two AND gate is disable, so the data input D3 input line is selected and transmitted as output. Hence, the output Y = D3. And so on.

Truth Table of 4-to-1 Multiplexer

 S0 S1 D0 D1 D2 D3 Y 0 0 0 X X X 0 0 0 1 X X X 1 0 1 X 0 X X 0 0 1 X 1 X X 1 1 0 X X 0 X 0 1 0 X X 1 X 1 1 1 X X X 0 0 1 1 X X X 1 1

We can write the Boolean expressions from the above truth table.

Y = S0’ S1’ D0 + S0’ S1 D1 + S0 S1’ D2 + S0’ S1’ D3

### 8-to-1 Multiplexer

#### 8-to-1 Multiplexer Circuit Diagram

An 8-to-1 multiplexer is a combination digital multiplexer circuit. The 8-to-1 multiplexer has an eight data inputs line, three select lines and one output line. For implement an 8-to-1 MUX logic circuit we need 8 AND gates, an OR gate, and a 3 NOT gate.

8 to 1 MUX have eight inputs line these input lines are D0, D1, D2, D3, D4, D5, D6, and D7, three data select lines they are S0, S1, and S2. 8-inputs represent 2m = 23 data select lines. These data select line select controlled particular input lines.

The logic symbol, switching circuit analogy and block diagram of 8-to-1 multiplexer figure shown below. 8-to-1 MUX

#### 8 to 1 Multiplexer Working Principle

• When all select input line are S0=0 S1=0, S2=0, then the topmost AND logic gates is enable and all other AND logic gates are disable so the data input D0 is selected and transmitted as output. The output is Y = D0.
• When all select input line are S0=1 S1=1, S2=, then the topmost AND logic gates is disable and all other AND logic gates are enable so the data input D7 is selected and transmitted as output. The output is Y = D7.

#### Truth table of 8 to 1 Multiplexer is given below.

 S0 S1 S2 D0 D1 D2 D3 D4 D5 D6 D7 Y 0 0 0 0 X X X X X X X 0 0 0 0 1 X X X X X X X 1 0 0 1 X 0 X X X X X X 0 0 0 1 X 1 X X X X X X 1 0 1 0 X X 0 X X X X X 0 0 1 0 X X 1 X X X X X 1 0 1 1 X X X 0 X X X X 0 0 1 1 X X X 1 X X X X 1 1 0 0 X X X X 0 X X X 0 1 0 0 X X X X 1 X X X 1 1 0 1 X X X X X 0 X X 0 1 0 1 X X X X X 1 X X 1 1 1 0 X X X X X X 0 X 0 1 1 0 X X X X X X 1 X 1 1 1 1 X X X X X X X 0 0 1 1 1 X X X X X X X 1 1

The Boolean equation is obtained from the above truth table for the output is given as:

Y = S0’ S1’ S2‘ D0 + S0’ S1‘ S2 D1 + S0‘S1 S2‘ D2 + S0’ S1 S2 D3 +S0 S1’ S2’ D4 + S0 S1’ S2 D5 + S0 S1 S2’ D6 + S0 S1 S2 D7

### 16-to-1 Multiplexer

The higher order multiplexer like 8-to-1, 16-to-1, etc. can be implemented by using lower order of multiplexer. IC74150 is a 16-to-1 multiplexer IC. It has 16 input lines these are D0, D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D12, D13, D14 and D15, four data select lines S0 S1 S2 andS3, and one output line Y.

The following image shows the IC 74150 and block diagram of 16-to-1 Multiplexer. Truth table for 16-to-1 Multiplexer is shown below

 S0 S1 S2 S3 Y 0 0 0 0 D0 0 0 0 1 D1 0 0 1 0 D2 0 0 1 1 D3 0 1 0 0 D4 0 1 0 1 D5 0 1 1 0 D6 0 1 1 1 D7 1 0 0 0 D8 1 0 0 1 D9 1 0 1 0 D10 1 0 1 1 D11 1 1 0 0 D12 1 1 0 1 D13 1 1 1 0 D14 1 1 1 1 D15

The Boolean Expression of a 16-to-1 Multiplexer are:

Y= S0‘S1‘ S2‘ S3‘ D0 + S0‘ S1‘ S2‘ S3 D1+ S0‘ S1‘ S2 S3‘ D2+ S0 S1‘ S2‘ S3 D3+ S0‘ S1 S2‘ S3‘ D4+ S0‘ S1 S2‘ S3 D5+ S0‘ S1 S2 S3‘ D6+ S0‘ S1 S2 S3 D7+ S0 S1‘ S2‘ S3‘ D8+ S0 S1‘ S2‘ S3 D9+ S0 S1‘ S2 S3‘ D10+ S0 S1‘ S2 S3 D11+ S0 S1 S2‘ S3‘ D12+ S0 S1 S2‘ S3 D13+ S0 S1 S2 S3‘ D14+ S0 S1 S2 S3 D15

Logical circuit diagram of a 16-to-1 Multiplexer is shown below. 16-to-1MUX can be implemented by using lower order of multiplexer like 8-to-1 and 2-to-1. • It reduce the no of wires
• It reduces the cost of circuit and complexity of the circuit.
• The number of combinational circuit can be implemented by using multiplexer.
• It doesn’t require simplification and K-map
• It makes transmission circuit economical and les complex
• It improves the reliability of digital system and reduces the number of exterior wired connections
• Logic circuit can be simplified by using MUX

• Additional delay required in switching port.
• It has some limitation of port utilization at same time.
• Using of additional I/O port to controlling of multiplexer.

### Applications of Multiplexers

Multiplexers are used in various types of applications

Communication System:- In communication system, the transmission data efficiency of communication system can be increase by using multiplexer. Such audio and video data through a single line.

Computer Memory:- In computer memory, to maintain the huge amount of memory by used multiplexer. It reduces the copper lines requirement to connect the other part of memory.

Telephone Network:- Multiple voice signals are integrated by using multiplexer technique.

Computer System of a Satellite system:- Transmission of signals from computer system to satellite system.

## What is Demultiplexer?

Demultiplexer is an also a combinational circuit in which one input and more than two output. The demultiplexer is a reverse process of multiplexer. ### Types of Demultiplexer

• 1-2 demultiplexer
• 1-4 demultiplexer
• 1-8 demultiplexer
• 1-16 demultiplexer

• A demultiplexer separates the two mutual signals.
• The operation of demultiplexer is reverse of the operation of multiplexer.
• In audio and video transmission we need a MUX and DEMUX.
• It decode the security systems.

• Wastage of Bandwidth
• Synchronization of the signals

### Applications of Demultiplexer

• It is use in Communication System for process of data separation.
• For store the output of Arithmetic Logic Unit in multiple register.
• DEMUX are used in Serial to Parallel Converter.

### Difference between Multiplexer and Demultiplexer

#### Multiplexer

• It is a combinational circuit in which have several input and one output.
• It is a digital switching circuit.
• It is a parallel to serial converter.
• The multiplexer used in TDM.
• 8-1 MUX, 16-1 MUX, and 32-1 MUX are the different type of MUX
• In multiplexer, the selection lines are used to control the specific input.

#### Demultiplexer

• It is a combination circuit.
• It has one input and several outputs.
• It is a data distributer.
• The serial to parallel conversion.
• It works on the principle of one-to-many.
• The various types of demultiplexers are 1-8 Demux, 1-16 Demux, 1-32 Demux.