$[10/10/10/15]$ 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 com$$ puter having an LI 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, $1$ cycle; cache miss, $110$ cycles; main memory access with cache disabled, $105$ cycles.

a$.[10]$ When you run a program with an overall miss rate of $3\%,$ what will the average memory access time $($in CPU cycles$)$ be$?$

b$.[10]$ 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 $1$ GB $($all of which 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 $64$ KB$,$ what will the average memory access time be$?$