For all cases below,

$$ The cache can hold $128$ kB$.$

$$ Data are transferred between main memory and the cache in blocks of $32$ bytes each.

$$ The byte addressable main memory consists of $64$ MB$.$

Explain the format of main memory address & size of comparator logic if

a$)$ b$)$ c$)$ Direct Mapped Cache is used

Full Associative cache is used.

$8-$way set$-$associative cache is used.

In each case clearly mention all fields of address $($i$.$e$.$ main memory & cache side$).$

b$)$ Fully$-$associative cache

c$)4-$way set associative cache