1. [5] You are trying to appreciate how important the principle of locality is in justifying the use of a cache memory, so you experiment with a computer having an L1 data cache and a main memory (you exclusively focus on data accesses). The latencies (in CPU cycles) of the different kinds of accesses are as follows: cache hit, 5 cycle; miss penalty, 120 cycles; main memory access with cache disabled, 120 cycles.

a. When you run a program with an overall miss rate of 3%, what will the average memory access time (in CPU cycles) be?

b. Next, you run a program specifically designed to produce completely random data addresses with no locality. Toward that end, you use an array of size 2 MB (all of it fits in the main memory). Accesses to random elements of this array are continuously made (using a uniform random number generator to generate the elements indices). If your data cache size is 32 KB, what will the average memory access time be?

c. If you compare the result obtained in part (b) with the main memory access time when the cache is disabled, what can you conclude about the role of the principle of locality in justifying the use of cache memory?