Consider a computer system with a $2-$way set associative cache and the following specifications:

$$ Cache size: $64$ KB

$$ Main memory size: $32$ MB

$$ Block size: $32$ bytes Calculate the following:

$($a$)$ The number of sets in the cache.

$($b$)$ The number of bits required for the offset.

$($c$)$ The number of bits required for the set index.

$($d$)$ The number of bits required for the tag.

$($e$)$ The total number of bits in a cache address.