Implementation of AND Gate from NOR Gate

Digital electronics revolves around storing data in bits of 1s and 0s. Not only is digital electronics an efficient way of storing data but it also makes it easier to encrypt and secure our data. It is awesome how we can use different logic gates to implement some functions and represent these equations.
In this article, we will see how we can represent an AND logic which is high using a NOR logic which represents complement. Firstly, we will individually understand these gates and then we will implement them.

What is an AND Gate?

An AND gate is a basic gate that is popularly known as an all-or-nothing gate. It gives one input when fed with two or more than two inputs. It is important to note that the output of the AND gate becomes low even if any one of the inputs is low and it becomes otherwise. Therefore it functions in a way that it is high only when all its inputs are high or ‘1’.

Let us see the AND gate for two inputs :

Y=A.B

where . represents AND

Here is a truth table which helps us analyze what will be the output of AND for different A and B fed to it

AND Gate

What is a NOR Gate?

NOR is a universal logic gate that can be used to implement any other gate of digital electronics. NOR is made up of two words ‘NOT’ and ‘OR’ .This means that this gate inverts the output of ‘OR’ . We can write NOR as

NOR =OR +NOT

NOR gate is high only when all its input values are low. It is amazing how it gives low ‘0’ eve when all its inputs are high ‘1’.

Let us see the NOT gate for two inputs.

Y=(A+B)′

where Y is equal to A plus B whole bar

Here is a truth table which helps us analyze what will be the output of NOR for different A and B fed to it.

NOR Gate

Implementation of AND Gate From NOR Gate

Now we have to see how can we use NOR gate to create the logic of AND gate. Note that if we take 3 NOR gates where we use the first two NOR gate to invert the input values and use the third NOR gate to to invert the output of previous two NOR gates ,we will get an output which will be equal to AND of the two input variables. Let us see the implementation below

Implementation of AND using NOR

The output of first two NOR gates

Y₁=A’ and Y₂=B’

The output of first third NOR gate

Y=(A’+B’)’=(A’)’.(B’)’

∴ Y=A.B

Since the final output is the output of AND gate means our realization of circuit is correct and we build the correct circuit.

Conclusion

Here we saw how we can use a basic gate called ‘NOR’ gate to implement ‘AND’ gate .This is important as it helps us analyse the working behind basic gates and we can understand how we can implement it using other gates. This is a basic level implementation of gates and there can be many more complex realization using other basic gates. It is advised that readers go through all other realization to understand the basic functioning behind other important gates. Some Frequently Asked Questions have been answered that cover some other basic concepts .Readers can refer to these questions as well.

Implementation of AND Gate From NOR Gate – FAQs

What are universal gates and why are they called so?

NAND and NOR gate are called universal gates because they can be used to generate all possible combinational logic functions

What are all the possible gates in Digital Electronics?

There are seven basic logic gates and these are AND, OR, XOR, NOT, NAND, NOR and XNOR

What is realization of a circuit in Digital Electronics?

Realization is the process of making different gates using the combination of given gates or diodes. The word ‘realise’ here means to implement an equation using the logic gates.