Final answer:
The Exclusive OR (^) operator is a Boolean operator that outputs true only when the inputs differ. It is extensively used in computing and digital circuits for performing calculations that involve decision-making processes.
Step-by-step explanation:
The Exclusive OR (^) operator, also known as XOR, is a type of Boolean operator used in various computing fields such as digital electronics, computer science, and mathematical logic. The XOR operator outputs true only when the inputs differ (one is true, the other is false). In the context of Boolean algebra, if you have two inputs, A and B, the XOR operation can be represented as (A AND NOT B) OR (NOT A AND B), meaning it gives a true output when either A or B is true, but not both.
For instance, in binary operations, if A is 0 and B is 1, then A XOR B would be 1, because they are different. But if both A and B are 0 or both are 1, then A XOR B would be 0, as the inputs are not exclusive. This principle is commonly used to perform calculations in computer programming and digital circuits where decision-making processes are involved.