A processor accesses main memory with an average access time of T2. A smaller cache memory is

interposed between the processor and main memory. The cache has

a significantly faster access time of T1 T2.

The cache holds, at any time, copies of some main memory words and is designed so that the words more likely to

be accessed in the near future are in the cache. Assume that the probability that the next word ac

cessed by the

processor is in the cache is H, known as the hit ratio.

a

. For any single memory access, what is the theoretical speedup of accessing the word in the cache rather

than in main memory?

(

5

)

b.

Let T be the average access time. Express T as a functi

on of T1, T2, and H.What is the overall speedup

as a function of H?

(

5

)

c.

In practice, a system may be designed so that the processor must first access the cache to determine if

the word is in the cache and, if it is not, then access main memory, so that on a

miss (opposite of a hit),

memory access time is T1 T2. Express T as a function of T1, T2, and H. Now calculate the speedup and

compare to the result produced in part (b)