A memory has $32-$bit addresses. It also has a $256KB$ cache. Blocks are $64$ bytes in size. Note $1K=2^{10},1M$

$=2^{20}$

a$.$ How many blocks are there in the cache if the cache is a direct$-$mapped cache?

b$.$ How many sets are there in the cache if the cache is a $2-$way set$-$associative cache?

c$.$ Show the partitioning of a memory address into the appropriate fields, if the cache is a direct$-$mapped

cache, and $2-$way set associative, respectively. That is to find how many bits needed for tag, block$/$set

index and byte offset, respectively.

d$.$ What is the total size of the cache if the cache is a direct$-$mapped cache?

e$.$ What is the total size of the cache if the cache is a $2-$way set associative cache?