Implementation of NOR gate using 2 : 1 Mux

In Digital Electronics, the concepts of Gates and Mux are a must to design the Digital circuit. The gates are the building block in Digital electronics and a MUX is a combinational logic circuit used in Digital Electronics. By Combining different types of gates we can design a complex circuit that can be used to perform a specific task. Through a combination of Digital circuits, we can design a circuit that can perform arithmetic operations or we can create a circuit that can Perform specific logical operations as per our Requirements.

In this article, we will be going through the implementation of the NOR gate using 2: 1 Mux, First, we will go through the basics of the NOR gate and Multiplexer in Depth and we will understand the Circuit, Symbol, Block Diagram, and Truth Table. Then we will see how we can Implement of NOR gate using 2: 1 Mux. At last, we will conclude our Article with some FAQs.

What is a Multiplexer?

A Multiplexer which is also MUX is a Combinational logical Circuit in Digital Electronics. The Mux has multiple input lines, a single output line, and several select lines. It is Used to Select one of the many input signals and route it to a single output line that’s why it is also called a Data Selector. In Mux there are 2ⁿ  Input lines and a single output line where n is the number of Select lines. The Multiplexers are used for Various Applications Such as data routing, Signal Selection, Data Compression, and parallel-to-serial conversion.

Multiplexer

What is 2:1 MUX?

2:1 MUX is a type of Multiplexer which has two input lines and one output line with one Select line.it is most simple and Fundamental type of the Multiplexer.

Components of 2:1 MUX

• There are two input lines,
• There is one output line, where the selected input will appear.
• There is one select line, also known as the control line, which determines which input is selected for the output.

2:1 Multiplexer

The Output will be selected using Select line S₀,So when S₀ will 0 input line I₀ will be routed and When S₀ will 1 I₁ will be routed.

Expression for 2:1 MUX

The Expression for 2:1 MUX can be Written as

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

Logical Circuit of 2:1 MUX

Given Below is the Logical Circuit for 2:1 MUX

Logical Circuit of 2:1 Mux

What is NOR Gate?

The NOR gate is the Fundamental and the universal gate in Digital Electronics. The NOR can also abbreviated as NOT-OR. The NOR gate can have two or more inputs and has a single Output. NOR gates are widely used in Digital electronics for building blocks for logical circuits such as flip-flops, registers, and other circuits. They can be combined to implement various logical functions and operations such as Full adder which we will be going through in this Article.

Types of NOR Gate

2 Input NOR Gate

In this NOR gate there is Two input terminal and a single output output terminal. The output is true only when both of its input terminals are false.

• If both inputs A and B are 0, the output is 1 (true).
• If either input A or input B (or both) is 1, the output is 0 (false).

2 Input NOR Gate

The Algebraic expression for the 2-input NOR gate can be Written as

[Tex]O=\overline{A+B}[/Tex]

Where, A and B are the Inputs and O is the Output

3 Inputs or Multi Input NOR Gate

In this type of NOR Gate there is three or more input terminals. The output of a multi-input NOR gate is true (logic 1) only when all of its input terminals are false (logic 0).

• The output is 1 (true) only when all input signals are 0.
• If any of the inputs are 1, the output is 0 (false).

3 Inputs Input NOR Gate

The Algebraic expression of 3 Inputs or Multi Input NOR Gate can be written as

[Tex]O=\overline{A+B+C}[/Tex]

Where A,B,C are inputs and O is the Output

Truth Table of 3 Inputs or Multi Input

The Truth Table of the Truth Table of 3 Inputs or Multi Input can be written as

Input A	Input B	Input C	Output O
0	0	0	1
0	0	1	0
0	1	0	0
0	1	1	0
1	0	0	0
1	0	1	0
1	1	0	0
1	1	1	0

Implementation of NOR gate using 2 : 1 Mux

Implementation of NOR gate using 2 : 1 Mux is done by taking a multiplexer which is having 2 input lines, one output line and one select or control line which determines which input is selected for the output.

Given below is the Logic Diagram of the Implementation of the Implementation of NOR gate using 2 : 1 Mux :

Implementation of NOR gate using 2 : 1 Mux

• The Expression of NOR gate is [Tex]\overline{A+B}[/Tex] which can be written as [Tex]\overline{A}.\overline{B}[/Tex] using de morgan’s theorem So to obtain the Expression of NOR gate let us Put A in the Expression of the 2:1 MUX.
• The Expression can be Written as [Tex]\overline{A}.I_0+\overline{A}.I_1[/Tex],Now substitute I₀ and I₁ with [Tex]\overline{B} [/Tex]and 0.
• So the new Expression can be written as [Tex]\overline{A}.\overline{B}+0.I_1=\overline{A}.\overline{B}[/Tex] this how we can Obtain the Mathematical Expression for NOR gate for 2:1 Mux.
• So, In the Circuit First 2:1 Mux is Used to get  [Tex]\overline{B}[/Tex],This can be achieved by giving Input 1 and 0 as a Input to the MUX and Selecting Select Line as B.
• Now in the Second [Tex]\overline{B}[/Tex] and 0 is given as the Input and A is selected as the select line and with this arrangement we get our NOR gate from 2:1 Mux.

Conclusion

In this Article, we have gone through the basic Concept of NOR gate and 2:1 With its Circuit diagram, Truth Table, Logical Expression.. Also we have gone through the Implementation of NOR Gate using 2 : 1 MUX which is an important concept in Digital Electronics for designing and Building the Circuits.

Implementation of NOR gate using 2 : 1 Mux – FAQs

What is the purpose of a Multiplexer (MUX) in digital circuits?

A Multiplexer is used to select one of many input signals and route it to a single output line based on the state of select lines. It serves as a data selector, enabling efficient data routing and signal selection in digital systems.

What are the advantages of using a MUX-based implementation of a NOR gate?

Using a MUX-based implementation provides efficiency in circuit design. It allows for the integration of multiple logic functions into a single component, reducing the overall complexity of the circuit. MUX-based designs can be more easily optimized and scaled compared to traditional gate-based implementations.

Can multiplexers be cascaded or combined to create larger multiplexers?

Yes, multiple multiplexers can be cascaded or combined to create larger multiplexers with a greater number of input lines and select lines. This enables the handling of more complex data routing and signal selection tasks in digital systems.