An XOR gate, short for Exclusive OR gate, is a digital logic gate that performs the logical XOR operation on two binary inputs to produce a single binary output. The output of an XOR gate is high (1) when the number of high inputs is odd; otherwise, the output is low (0). In other words, the output is high if the inputs are different from each other.

The logic symbol for an XOR gate is represented as follows:

   ----       ----
A |    |    B |    |
  | XOR |      |    |
---|    |    ---|    |
   ----       ----
     Output

In this symbol:

  • A and B represent the input signals.
  • The XOR symbol in the middle represents the logical XOR operation.
  • The output is the result of the XOR operation.

The truth table for a 2-input XOR gate is as follows:

ABOutput
000
011
101
110

The truth table shows the output for all possible combinations of input values. As per the truth table, the output is 1 when the inputs are different; otherwise, the output is 0.

XOR gates have various applications in digital systems, including:

  • Binary addition and subtraction.
  • Parity checking to detect errors in data transmission.
  • Implementing logical functions that involve odd numbers of true inputs.
  • Arithmetic logic units (ALUs) in processors for mathematical operations.
  • Cryptography for encryption and decryption operations.

By combining XOR gates with other logic gates, more complex logic functions and digital circuits can be designed to perform various tasks in electronic devices and systems.