Definition of XOR

Definition:

XOR is a binary operation like AND and OR. If two bits are XORed together the results are as follows.

 A B --- A XOR B
 0 0 ----- 0
 0 1 ----- 1
 1 0 ----- 1
 1 1 ----- 0
 

Another way to express this is that the result is true if they are different or false if they are the same.

Useful Property

Mathematically, XOR is both associative and commutative. What this means is that if

 C = A xor B
 then
 B = C xor A or
 B = A xor C
 

and

 A = B xor C
 A = C xor B
 

This can be used to disguise text.

 'A' xor 0x5516 = 0x1416
 

By Xoring this value with 0x55₁₆ again the original value 'A' is recovered.

In C, C++ and C# binary XOR is represented by a single character ^.

 int c = a^b; 

Glossary:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Alternate Spellings: Exclusive OR