A $$CPU$$ has $$32$$-bit memory address and a $$256$$ $$KB$$ cache memory. The cache is organized as a $$4$$-way set associative cache with cache block size of $$16$$ bytes.

(a)$$\,\,\,\,$$ What is the number of sets in the cache?
(b)$$\,\,\,\,$$ What is the size (in bits) of the tag field per cache block?
(c)$$\,\,\,\,$$ What is the number and size of comparators required for tag matching?
(d)$$\,\,\,\,$$ How many address bits are required to find the byte offset within a cache block?
(e)$$\,\,\,\,$$ What is the total amount of extra memory (in bytes) required for the tag bits?

A computer system has a three level memory hierarchy, with access time and hit ratios as shown below:

(i) What should be the minimum size of level $$1$$ and $$2$$ memories to achieve an average access time of less than $$100$$ nsec?

(ii) What is the average access time achieved using the chosen sizes of level $$1$$ and level $$2$$ memories?