Exercise 2: RAID

Review Modulo-2 Sums

• commutative law: x ⊕ y = y ⊕ x
• associative law: x ⊕ ( y ⊕ z) = (x ⊕ y ) ⊕ z
• identity: x ⊕ 0 = x
• itself is the inverse: x ⊕ x = 0
• corollary: if x ⊕ y = z, then adding x to both sides: y = x ⊕ z

1.Parity Bits

From DSCB Ex 13.4.1. Compute the parity bit for the following bit sequences:

a) 00111011

b) 00000000

c) 10101101

2. Recovery using parity blocks

From DSCB Ex 13.4.6. Suppose we are using a RAID level 4 scheme with four data disks and one redundant disk. As in Example 13.9 assume blocks are a single byte. Give the block of the redundant disk if the corresponding blocks of the data disks are

a) 01010110, 11000000, 00111011, 11111011

b) 11110000, 11111000, 00111111, 00000001

From DSCB Ex.13.4.7. Using the same RAID level 4 scheme as in Ex.13.4.6 suppose that the data disk 1 has failed. Recover the block of that disk under the following circumstances:

c) The contents of disks 2 through 4 are 01010110, 11000000, and 00111011, while the redundant disk holds 11111011.

d) The contents of disks 2 through 4 are 11110000, 11111000, and 00111111, while the redundant disk holds 00000001.