Uses of Exclusive OR

• Hashing: hash functions are closely related to encryption.

• Graphics: background ⊕ picture paints picture, but another ⊕ picture erases it and restores background. This is especially good for animation and for cursors, which move across a background.

• Linked lists: both forward and backward pointers can be stored in the same space using next ⊕ previous. Since we will be coming from either next or previous, we can ⊕ with the link value to get the other one.

• RAID[redundant array of independent disks]: a disk that stores (a ⊕ b) can back up two other disks, a and b. If a fails, b ⊕ (a ⊕ b) = a; if b fails, a ⊕ (a ⊕ b) = b.

• Wireless networking: if message (a ⊕ b) is broadcast, those who know a can get b, and those who know b can get a.