Understanding Exclusive OR (XOR): A Logical Operation for Computer Science and Mathematics

exclusive or

Exclusive or, often abbreviated as XOR, is a logical operation that outputs true only when the number of true inputs is odd

Exclusive or, often abbreviated as XOR, is a logical operation that outputs true only when the number of true inputs is odd. It is commonly used in computer science and mathematics.

In terms of truth values, exclusive or can be defined as follows:

– If both inputs are true, the output is false.
– If both inputs are false, the output is false.
– If one input is true and the other input is false, the output is true.
– If one input is false and the other input is true, the output is true.

This can be represented using a truth table:

| Input A | Input B | Output |
|———|———|——–|
| true | true | false |
| true | false | true |
| false | true | true |
| false | false | false |

Exclusive or can also be represented symbolically using the caret symbol (^) or the plus symbol (+), depending on the context. For example, A XOR B can be written as A ^ B or A + B.

In programming, exclusive or is often used to perform bitwise operations on binary numbers or to express conditional statements where only one of multiple conditions can be true.

Here is an example of how exclusive or can be used in binary operations:

| Binary A | Binary B | XOR Result |
|———-|———-|————|
| 1010 | 1100 | 0110 |
| 0101 | 0011 | 0110 |

In the above examples, each digit of the binary numbers is compared. If the digits are the same, the XOR result is 0, and if they are different, the XOR result is 1.

Overall, exclusive or is a fundamental concept in logic and computer science, and understanding how it works can be useful in various mathematical and computational applications.

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