You are asked to perform capacity planning for a two-level memory system. The first level, Ml, is a cache with three capacity choices of 64 Kbytes, 128 Kbytes, and 256 Kbytes. The second level, M2, is a main memory with 4 Mbytes in capacity. Let C1, and C2 be the costs per byte and t1, and t2 the access times for Ml and M2, respectively. Assume C1 = 2OC2 and t2 = 10tl. The cache hit ratios for the three capacities are assumed to be 0.7, 0.9, and 0.98, respectively.

(a) What is the average access time ta, in terms of t1= 20 ns in the three cache designs? (Note that t1 is the time from CPU to Ml and t2 is that from CPU to M2, not from Ml to M2).

(b) Express the average byte cost of the entire memory hierarchy if C2 = $0.2/Kbyte.

(c) Compare the three memory designs and indicate the order of merit in terms of average costs and average access times, respectively. Choose the optimal design based on the product of average cost and average access time.