In block RAID systems $($e$.$g$.,$ RAID$-4$ or RAID$-5)$ the parity block is computed from all of the

data blocks:

$A_p=A_{1}o+A_{2}o+A_{3}o+$cdotso$+A_n$

where $o+$ is xOR,$A_i$ is a data block and $A_p$ is the parity block.

If a data block is rewritten, the parity block must also be updated. However, I claim that you

do not have to redo the entire calculation. If $A_d$ is the old value of a data block, $A_d^{\text{'}}$ is the new

value of the data block and $A_p^{\text{'}}$ is the new value of the parity block, show that

$A_p^{\text{'}}=A_{p}o+A_{d}o+A_d^{\text{'}}$

Hints:

$o+$ is commutative and associative

What is $xo+x?$

What is $xo+0?$