Implementation of NAND Gate using 2 : 1 MUX

In electronics Engineering, Understanding the Concepts of MUX and Logic gates is very important. These components are the building blocks for designing and Constructing complex digital circuits. Multiplexer is a versatile device that plays an important role in data routing and Selection. It enables the selection of one of the several input signals and routing it to the single output based on the control Signal. The logic gate takes one or more Binary inputs and performs logical operations on them to produce a single binary output.

In this article, we will be going through the Implementation of the NAND Gate using 2: 1 MUX, First, we will start our Article with a Brief Introduction to the 2:1 MUX and NAND Gate. We will through the basic Concepts of both of these with their truth table. Then we will see how we can Implement the NAND gate using 2:1 MUX.

What is a Multiplexer?

A Multiplexer(MUX) which is also called Data Selector, is a Fundamental Component in Digital Electronics. It is a Combinational logic circuit that has multiple input line, one output line, and Several select lines. It works on the principle of taking many inputs and providing a single output (many to one). The main function of the Multiplexer is to select one of its input lines from multiple lines and send it to the output line based on the State of the Select line provided. In Multiplex there are 2ⁿ  Input lines and Single output lines. In 2ⁿ lines n is the number of the select lines. Multiplexers are used for Various Applications such as data routing, signal routing, and control logic in digital circuits.

Multiplexer

What is 2:1 Multiplexer?

In 2:1 MUX is there is 2 Input lines and and single output Y with One Select line .The number of Select line is Decided using 2ⁿ where n is the number of Select lines. Here the input lines will two so the select line will be one as 2¹

As we Know the output of the MUX is decided using Select Line. So, the Select line S₀ will have Two values 0 and 1.When the S₀ will be 0 the Input line will be Selected and When the S₀ will be 1 the input line will be selected.

2:1 Multiplexer

Truth Table 2:1 Multiplexer

From the Truth table the Expression for the 2:1 Mux can Be derived as

So for the Circuit for this expression can be designed as

2:1 Multiplexer

What is NAND Gate ?

The NAND gate is one of the Universal and Fundamental gate in the digital Electronics. It can be called as the combination of NOT and AND gate. It can Take Two or more inputs and Provide a Single Output. NAND gate can be represented as AND gate with a small circle at its output which indicates the inversion. A NAND gate outputs 1 only if all of its inputs are 0. If any input is 1, the output is 0.

Two Input NAND Gate

In this NAND gate there is two input and a single output. Its output is high (1) when at least one of its inputs is low (0); otherwise, the output is low (0).

2 Input NAND Gate

Its Expression can be written as

X=

where X is the output and A and B is the input

Three or More Input NAND Gate

In this NAND gate the input can be three or more. Its output is low (0) only when all of its inputs are high (1); otherwise, the output is high (1).

3 Input NAND Gate

Expression of Three or more Input NAND Gate can be written as

X=

Where, X is the output and A ,B and C is the input

Implementation of NAND Gate using 2 : 1 MUX

Now We will go through the Implementation of the NAND Gate using 2:1 MUX. The Follow Circuit Shows the Implementation of NAND gate using 2:1 MUX

Implementation of NAND Gate using 2 : 1 MUX

• The Expression of NAND gate can be written as ,So to obtain this Expression from the MUX, First we will Select line of MUX as Any Input of NAND gate(Let us take A)
• So, Now the Expression can be Written as ,In this Expression Instead of Input lines I₀ and I₁ ,let us take 1 and .Expression can be Written as using boolean algebra Y can Be Written as (Using de morgans’s Theorem),This is How we can Mathematical Represent the NAND gate using 2:1 MUX.
• So, In the Circuit First 2:1 Mux is Used to get ,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 2:1 Mux 1 and is given as a Input and A is selected as Select line. So, the output of the mux will be which is the expression of the NAND gate.
  

So, This is how we can Implement NAND gate using 2:1 MUX

Conclusion

In this Article, we have gone through the Important concept of the NAND gate and MUX which are very much important in the Digital Electronics. We have Seen their Working Principle, Types, Truth Table and their Symbolic representation. Also we have gone through the Implementation of NAND Gate using 2 : 1 MUX which is an important concept in Digital Electronics for designing and Building the Circuits.

Implementation of NAND Gate using 2 : 1 MUX – FAQs

Why is the NAND gate considered a universal gate?

The NAND gate can be used to implement any other logic gate, including AND, OR, and NOT gates. Therefore, it is considered universal in digital logic design.

Can MUX be cascaded to select from more than two inputs?

Yes, MUX can be cascaded together to select from more than two inputs. This allows for more selection of data in digital circuits.

How does the delay of a MUX affect the performance of a digital circuit?

The delay of a MUX, which is the time it takes for the selected input to appear at the output, impacts the overall speed and efficiency of a digital circuit. Lower delay results in faster data processing.