Operating systems

1. Background: Consider a disk with 8 sectors per track. Without interleaving, the sequence of sector numbers going around the track would be 0-1-2-3-4-5-6-7. In a uniform interleaving, you use every ith sector where the interval between successive sector numbers is a constant. The interleaving 0-2-4-6-1-3-5-7 is non-uniform because, while i=2 in most cases, the jump from 6 to 1 uses i-3 and the jump from 7 back to 0 uses i=1. The sequence given by l is usually described as non-interleaved, but technically, it is the simplest uniform interleaving. a) List all of the uniform interleavings on 8 sectors, and for each, state the value of i. (0.5 points) b) Give a general rule. If the disk has s sectors per track, what values of i give distinct uniform interleavings. (There is a formally correct mathematical description of the required relationship between s and i.) (0.5 points)