Parity

Parity is a sort of checksum of data that allows reconstruction of data that was lost. RAID, RAM and multicasting protocols make use of parity.

XOR Parity
One simple way to implement parity is to use XOR. Consider a RAID 5 where you have three disks with parity on one of the three disks. Consider that a byte on disk one has a value of 43 (hexadecimal) and a byte on disk two has a value of 98 (hexadecimal), the parity on disk three is the XOR'ed product of the prior two. 0x43 XOR 0x98 = 0xDB. Now pretend you lose disk two, you just XOR the parity with the remaining good disks and you reconstruct what disk two was. So: 0xDB XOR 0x43 = 0x98. Same concept if you had four disks, let's pretend it has a byte value of 15 (hexadecimal), So: 0x43 XOR 0x98 XOR 0x15 = 0xCE. If you lose disk one you XOR the XOR'ed product of the remaining disks with the parity so: (0x98 XOR 0x15) XOR 0xCE = 0x43.