How to calculate RAID Parity Bit? [closed]

Question

How do I calculate the parity bit? In a RAID 3 odd parity with 5 disks. How do I get the parity bit?

The answer was

But I want to know how is this calculated?

Answer 1

"Odd parity" means the sum of all the its is odd. This is the same as saying the number of 1 bits is odd. So if the number of one bits is odd, the parity bit must be 0 to keep it that way. If it's even, the parity bit must be 1 to make it odd.

Answer 2

The parity is calculated via a logical "exclusive-or" operation, XOR.

It results in true (1) if one or the other of the values that it's calculating on is true, but not if both are true - if neither or both values are true, the result is false (0). Using this logic, the array generates extra data that it is able to use to reconstruct the data on a lost disk.

The catch with odd-parity is that it's reversed - if the XOR operation results in a 1, a 0 is stored instead. I'm not 100% sure, but I don't believe that odd parity gets much use in the real world.

So, in the examples above, the second row:

1(disk0)       XOR 0(disk1) = 1
1(last result) XOR 1(disk2) = 0
0(last result) XOR 1(disk3) = 1 (result of the XOR across the entire row)

In odd parity, flip the result and that's the result bit; 0, in this case.

The reason that this is interesting and useful? Let's say disk 2 is lost, and you need to figure out what was in it.

1(parity bit from disk4) XOR 1(disk0) = 0
0(last result)           XOR 0(disk1) = 0
0(last result)           XOR 1(disk3) = 1 (calculated disk2 data)

Using the parity, data from a lost disk can be reconstructed with the data from the parity disk plus all of the other disks - this is the reason that this type of RAID group can tolerate the loss of any one disk, but will fail if a second disk fails.