(a) A processor cache, as shown in Figure 1.5, is discussed in Section 1.6. Suppose that execution time for a program is directly proportional to instruction access time and that access to an instruction in the cache is 20 times faster than access to an instruction in the main memory. Assume that a requested instruction is found in the cache with probability 0.96, and also assume that if an instruction is not found in the cache, it must first be fetched from the main memory to the cache and then fetched from the cache to be executed. Compute the ratio of program execution time without the cache to program execution time with the cache. This ratio is usually defined as the speedup factor 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.

LO1