Proof of Calculation of the Parity Block of RAID 4 and 5
In Section 2.5.4 we stated that during write operations the new parity block can be calculated from the old parity block and the difference Δ between the old data block D and the new data block . In the following we would like to present the proof for the example in Figure 2.16.
Mathematically speaking we state that:
Taking into account the calculation formula for the parity block we must therefore show that:
The associative law applies to the XOR operation so we do not need to insert any brackets.
We will conduct the proof on the basis of the values in Table A.1. The parity block will be calculated bit-by-bit by means of the XOR operation. The table therefore shows the occupancy of a bit (‘0’ or ‘1’) from the various blocks.
The left part of the table shows the possible occupancies for the bits in the old data block D, in the new data block and the parity bit for the bits in the remaining data blocks (A XOR B XOR C). The values of the individual blocks A, B, and C is insignificant because at the end of the day the ...