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Additional info for An Elementary Treatise on the Differential Calculus Founded on the Method of Rates or Fluxions

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L4 is determined by dividing the rotational time by the number of sectors per track; L2 is the base line and essentially goes through the y-axis at x = 0, L3 is just a head switch time above L2, and L4 a cylinder switch time above L2. The most difficult aspect of drawing the graph, then, is determining exactly where each point goes. A simple algorithm that counts how many sectors have been traversed by each skip is needed; when the total exceeds the number of sectors per track, one must plot a point on the head switch line (L2).

5 ms (when 1000 requests get spread across 2 disks, and each take 5 ms) and a high time of 5 ms (when all 1000 end up on the same disk). 6 a. 12 chunks. Divide the pattern size by chunk size. b. The 0th chunk and the 11th, the 1st and 10th, the 2nd and 9th, and so on. c. 6 disks. There are 12 chunks, and each chunk seems to be on the same disk as one other chunk. Hence, 12 divided by 2 gives us 6 disks. d. Start at the left, numbering chunks 0, 1, 2, . . , 5 across disks; then go to the next row, and instead number 11, 10, 9, .

Occupancy: Oread_memory = 20 c. occupancy: Osend_req = 1 d. occupancy: Osend_data = 4 e. occupancy: Osend_data = 4 f. occupancy: Osend_req + Orev_data = 1 + 4 = 5 g. 11 Chapter 4 Solutions ■ L-37 a. 29. 29 Table to specify the memory controller protocol. b. P1: read 110 P15: read 110 Read miss, P0 responds with data to P1 and memory Read miss, satisfied from memory P1’s read miss will force P0 to respond with data both to P1 and to memory and then transition to state S. The memory must receive the data and respond to all future requests.

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