A computer system has 256K words of main memory and 16K words of direct-mapped cache memory. The block size is 256 words. The access time for the main memory is 15 times that of the cache memory. assume that 1K = 1024 (that is 210) and 1M = 1024 X 1024 (that is, 220)

a) What is the size of the tag field?

b) If a fully associative mapping scheme were used instead, what would be size of the tag field?

c) Determine the efficiency of the system assuming a cache hit ratio of 0.9.

d) If the cache access time is 200 nanoseconds, what hit ratio would be required to

achieve an average access time equal to 500 nanoseconds?