Exclusive OR Gate

An  Exclusive OR gate(also named XOR, EOR, EXOR ) is a fundamental digital logic circuit that accepts two inputs and generates an output based on the exclusive OR operation applied to those inputs. The output of this gate is high or logic 1 when the inputs differ from each other; otherwise, it outputs logic 0.XOR gates are fundamental components in digital circuit design. They are widely used in arithmetic circuit operations, error detection systems, and cryptographic protocols because they can discern and manipulate binary signals based on their dissimilarity.

1.0Definition of Exclusive OR gate

This gate is obtained by using OR, AND, NOT gate. If one of the inputs is exclusively 1, then its output is 1. XOR produces a "1" output if the inputs differ and a "0" if all the inputs are the same value. The XOR checks the Exclusivity in the values of two input signals, A and B. If A and B are not identical such that (A=0 and B=1 and vice- versa the output obtained is  Y = 1, and if both are identical (A=0, B=0 Or A=1, B=1), the output obtained  Y =0. The operation thus is called exclusive OR gate or Designated EXOR. It is implemented by using transistors as an electrical switch for implementing Boolean Functions.  XOR is generally used in arithmetic logic circuits.

2.0Examples of XOR gates

• To perform arithmetic operations
• Game show buzzer
• Error Detection
• Comparing two logic levels.

3.0Boolean Expression of XOR gate

                         Y = A ⊕ B

4.0Symbol of XOR Gate

5.0 XOR Gate Circuit Diagram

6.0Truth Table of XOR Gate

7.0Applications of XOR Gate

• It is used in Data Encryption for security purposes.
• It is also used as a comparator circuit to check whether two binary values are equal.
• It is used in Arithmetic operations for Binary addition and subtraction.
• It is a fundamental building block of the cryptographic circuit.

8.0Properties of XOR Gate

• Inversion: It  Acts as a controlled inverter, and output follows the opposite input when one input is high.
• Addition Modulo 2: Performs binary addition without carry, which is crucial for arithmetic circuits.
• Error Detection: Used in error detection codes (ECCs) and checksums by XORing bits to detect data errors.
• Cryptographic Applications: Fundamental in encryption for secure data transmission.
• Building Block: Foundational in constructing complex logic circuits, providing precise control over signal states. 

9.0Solved Questions

Question: Write the symbol and Boolean Expression for the XOR gate.

Solution:  Symbol of XOR gates            

Boolean Expression of XOR gate

Y = A ⊕ B

Question: Write the Truth Table for the XOR gate.

Solution:

Question: State the condition when two input XOR gates produce a high output.

Solution: 

The Boolean expression of an XOR gate is Y = A ⊕ B. Using the Truth Table of an XOR gate; we say that a two-input XOR gate produces a high output when both inputs are different.

Question: A certain logic circuit has A and B as the two inputs; the output is given in the truth table. What is the logic gate in the circuit if the truth table of the circuit is given below:

Solution: According to the circuit's truth table, the gate is XOR gate.

Example: Find the logic equation as the staircase light is controlled by two switches, one at the top and the other at the bottom. At a particular point in time, is one switch ON while the other is OFF?

Solution: The logic Equation, according to this situation, is