What is an XOR Gate?

In digital electronics, the XOR (Exclusive-OR) Gate is a combination of all three fundamental or basic gates (NOT, AND and OR gates). It receives two or more than two input signals but produces only one output signal. It results in a low (0) if the input bit pattern contains an even number of high(1) signals. The output is high (1) for an odd number of high (1) signals in the input bit pattern.

The XOR gate’s behavior can be summarized as follows

Returns 1, if the number of logical high input is odd.

Returns 0. if number of logical high input is even.

The Boolean expression of two input XOR Gate is as follows

Say we have two inputs, A and B and the output is called X, then the expression is:

X = A⊕B = A’B + AB’

Logic Diagram of Two Input XOR Gate

The logic circuit diagram of the XOR gate is shown in the following figure. It has two input line denoted by the letter A and B and one output line denoted by the letter X, where X=A⊕B= A’B+AB’.

The Boolean expression of Three input XOR Gate is as follows

Truth Table of Two input XOR Gate

The truth table of two input XOR gate is given below. This table shows the relationship between two inputs and one output of the XOR gate. This also provides information about the operation of XOR gate for different input combinations.

Logic Diagram of Three Input XOR Gate

The logic circuit diagram of the XOR gate is shown in the following figure. It has three input line denoted by the letter A, B, C and one output line denoted by the letter X, where X=A⊕B⊕C.

The Boolean expression of N input XOR Gate is as follows:

Say we have N inputs, A_0, A₁, …., A_N and the output is called X, then the expression is:

X=A₀⊕A₁⊕…..⊕A_N.

Truth Table of Three input XOR Gate

The truth table of three input XOR gate is given below. This table shows the relationship between three inputs and one output of the XOR gate. This also provides information about the operation of XOR gate for different input combinations.

Say we have three inputs, A, B and C and the output is called X, then the expression is:

X = A⊕B⊕C

Logic Diagram of N input XOR Gate

The logic circuit diagram of the XOR gate is shown in the following figure. It has N input line denoted by the letter A₀, A₁, …., A_N and one output line denoted by the letter X, where X=A₀⊕A₁⊕…..⊕A_N.

Logic Gates are the building blocks of digital circuits, taking binary values as input and returning a binary value as output after performing a logical operation. There are several kinds of gates available in Digital Electronics like basic gates, and universal gates. Implementation of the XOR gate from the NAND gate is possible because the NAND gate is a Universal gate i.e., it can implement all other gates. The NAND gate gives the output 0 if all the inputs are 1 else it gives 1 for all other cases. XOR gate is a logic gate that gives output 1 when several 1s are odd else it gives 0. In this article, we will explore the XOR gate, and NAND gate and implement the XOR gate from the NAND gate.