Q$1.$ Consider the following:

Main memory size is $32KB,$ and Cache memory size is $4KB.$

Block size is $16$ bytes.

Fully associative mapping is used.

The access time of main memory is $10$ times that of the cache memory.

Cache hit ratio is $0\mathrm{.}9.$

a$)$ Find the length of the tag field.

b$)$ If a direct mapping were used, what would the length of the tag field?

c$)$ Calculate the access efficiency $($Access efficiency means the ratio of the average access tim

with a cache to the average access time without a cache$).$

d$)$ If the cache access time is $100ns,$ what hit ratio would be required to obtain an average

access time equal to $250$ ns$.$