Problem $2$: $(10$ points each, total: $20$ pts$)$ Cache Miss Analysis $($Compulsory$,$ Capacity, Conflict$)$

Consider a system with the following cache configuration:

$$ Cache Size: $16$ KB

$$ Block Size: $64$ bytes

$$ Associativity: $4-$way set associative

$$ Replacement Policy: LRU $($Least Recently Used$)$

A program accesses an array A of size $8$ KB $($where each element is $4$ bytes$)$ and iterates over the array multiple times. The array access pattern is sequential, and the program runs multiple iterations over A$.$

Questions:

$($a$)(10$ points$)$ Identify and describe the three types of cache misses$$compulsory$,$ capacity, and conflict misses$$that can occur when the array A is accessed. For each type, explain if it is likely to occur in this scenario and why.

$($b$)(10$ points$)$ Suppose the program is modified to access a larger array B of size $32$ KB$,$ again with each element being $4$ bytes. Analyze how the types of cache misses might change with the larger array. Specifically, identify which type of cache miss is most likely to increase and why.