Problem 2 (a) (4 pts) A processor cache is discussed in Section 1.2.2. Suppose that execution time for a program is proportional to instruction fetch time. Assume that fetching an instruction from the cache takes 1 time unit, but fetching it from the main memory takes 20 time units. Also, assume that a requested instruction is found in the cache with probability 0.9. Finally, assume that if an instruction is not found in the cache it must first be fetched from the main memory into the cache and then fetched from the cache to be executed. Compute the ratio of program execution time without the cache to program exccution time with the cache. This ratio is called the speedup resulting from the presence of the cache. (b) If the size of the cache is doubled, assume that the probability of not finding a requested instruction there is cut in half Repeat part (a) for a doubled cache size