Implementation of OR Gate from NOR Gate

An OR Gate is a basic logic gate that gives a HIGH or Logic 1 output, when any of its inputs is HIGH. Whereas, the NOR gate is a universal logic gate, which gives a HIGH output only when all its inputs are LOW or Logic 0. Before, going into the implementation of OR Gate using NOR Gate, let us discuss the basic theory of OR gate and NOR gate first.

What is an OR Gate?

An OR Gate is a basic logic gate. An OR gate can have two or more than two inputs, but has only one output. The OR gate gives a HIGH (Logic 1) output if any one of its inputs is in the HIGH or Logic 1 state, otherwise, it gives a LOW (Logic 0) state as output. Therefore, the output of the OR gate is LOW or Logic 0 state, only if all its inputs are LOW or Logic 0 state.

The OR gate is also known as an "any or all gate" or "an inclusive OR gate". The logic symbol of a two input OR gate is shown in Figure-1.

If variables A and B are the inputs to the OR gate and Y is the output variable, then the output equation of the OR gate is given by,

$$\mathrm{Y=A+B}$$

Where, the '+' symbol represents the OR operation. It is read as "Y is equal to A OR B".

The table that show the relationship between inputs and output of an OR gate is referred to as a truth table of the OR gate. The following is the truth table for the OR Gate.

Input		Output
A	B	Y = A + B
0	0	0
0	1	1
1	0	1
1	1	1

What is a NOR Gate?

NOR Gate is a universal logic gate, and hence it can be used for implementation of any other type of logic gate.

NOR means NOT + OR. That means, the OR output is NOTed or inverted. Therefore, the NOR gate is a combination of OR gate and a NOT gate, i.e.,

$$\mathrm{NOR\:\:Gate=OR\:\:Gate=NOT\:\:Gate}$$

A NOR gate is a type of logic gate whose output is HIGH (Logic 1), only when all its inputs are LOW (Logic 0), and it gives an output LOW (Logic 0), even if any of its inputs becomes HIGH (Logic 1). The logic symbol of a two input NOR gate is shown in Figure-2.

If variables A and B are the input variables to the NOR gate and Y is the output variable of the NOR gate, then the output of the NOR gate is given by,

$$\mathrm{Y=\overline{A+B}=(A+B)'}$$

It is read as "Y is equal to A plus B whole bar".

The following is the truth table of the NOR gate −

Input		Output
A	B	Y = (A + B)'
0	0	1
0	1	0
1	0	0
1	1	0

Now, let us discuss the implementation of OR Gate from NOR Gate.

Implementation of OR Gate from NOR Gate

As we know, the NOR gate is a type of universal logic gate, therefore, using NOR gates only, we can implement the OR operation. The logic diagram of OR Gate using NOR Gate is shown in Figure-3.

Hence, from the logic circuit, it is clear that we require only two NOR gates for the realization of OR operation.

The first NOR gate performs the NOR operation on variables A and B, thus the output of the first NOR gate is,

$$\mathrm{Y_1=\overline{A+B}}$$

The second NOR gates perform the NOT operation on the output of the first NOR gate. Therefore, the output of the second NOR gate is,

$$\mathrm{Y=A+B}$$

This is the output expression of an OR gate. Therefore, we can realize an OR gate using NOR gates only as shown in Figure-3.