org_roam/20260101011126-xor.org

xor

XOR stands for exclusive or. It is a logical operation that outputs true only when the inputs differ (one is true, the other is false). If both inputs are the same (both true or both false), the output is false.

Here is the truth table for XOR:

——-——-———

A

B

A XOR B

——-——-———

false

false

false

——-——-———

false

true

true

——-——-———

true

false

true

——-——-———

true

true

false

——-——-———

In programming, XOR is often represented by the caret symbol (^). For example, in many programming languages, you can use the XOR operator like this:

  a = True
  b = False
  result = a ^ b  # result will be True

In simple terms it means "one or the other, but not both".

Some similar concepts include:

• OR (inclusive or): Outputs true if at least one input is true.
• AND: Outputs true only if both inputs are true.
• NOT: Outputs the opposite of the input (true becomes false, false becomes true).
• NAND: Outputs false only if both inputs are true (the opposite of AND).
• NOR: Outputs true only if both inputs are false (the opposite of OR).
• XNOR: Outputs true only when both inputs are the same (the opposite of XOR).