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Parity bit
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=== RAID array === Parity data is used by RAID arrays ([[RAID|redundant array of independent/inexpensive disks]]) to achieve [[Redundancy (engineering)|redundancy]]. If a drive in the array fails, remaining data on the other drives can be combined with the parity data (using the Boolean [[XOR]] function) to reconstruct the missing data. For example, suppose two drives in a three-drive [[RAID 4]] array contained the following data: {| |- |Drive 1: |'''01101101''' |- |Drive 2: |'''11010100''' |} To calculate parity data for the two drives, an XOR is performed on their data: {| |- | |'''01101101''' |- | XOR |<ins>'''11010100'''</ins> |- | |'''10111001''' |} The resulting parity data, '''10111001''', is then stored on Drive 3. Should any of the three drives fail, the contents of the failed drive can be reconstructed on a replacement drive by subjecting the data from the remaining drives to the same XOR operation. If Drive 2 were to fail, its data could be rebuilt using the XOR results of the contents of the two remaining drives, Drive 1 and Drive 3: {| |- |Drive 1: |'''01101101''' |- |Drive 3: |'''10111001''' |} as follows: {| |- | || '''01101101''' || Drive 1 |- | XOR || <ins>'''10111001'''</ins> || Drive 3 |- | || '''11010100''' || Reconstructed Drive 2 |} The result of that XOR calculation yields Drive 2's contents. '''11010100''' is then stored on Drive 2, fully repairing the array. XOR logic is also equivalent to even parity (because ''a'' XOR ''b'' XOR ''c'' XOR ... may be treated as XOR(''a'',''b'',''c'',...), which is an n-ary operator that is true if and only if an odd number of arguments is true). So the same XOR concept above applies similarly to larger RAID arrays with parity, using any number of disks. In the case of a RAID 3 array of 12 drives, 11 drives participate in the XOR calculation shown above and yield a value that is then stored on the dedicated parity drive. Extensions and variations on the parity bit mechanism "double," "dual," or "diagonal" parity, are used in [[Non-standard RAID levels#RAID-DP|RAID-DP]].
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