$($cache$)$ Consider the following code: $(20$ points$)$

$(1)$ Assume that the system has a $8192-$byte, direct$-$mapped data cache with $16-$byte blocks.

Assuming that the cache starts from initial state $($i$.$e$.$ initially empty$),$ what is the series of data

cache hits and misses for the above code $($i$.$e$.$ number of misses and number of hits$)?$ Assume

that the ints are $32-$bits.

$(2)$ Assume that an iteration of a loop in which the load hits takes $10$ cycles but that an iteration of

a loop in which the load misses takes $100$ cycles. What is the execution time $($cycles$)$ of this

code with the aforementioned cache?

$(3)$ Repeat part $(1)$ except assume that the cache is $2-$way set associative with an LRU replacement

policy and $16-$byte sets $(8-$byte blocks$).$

$(4)$ Repeat part $(2)$ using the cache described in part $(3).$ Is the direct$-$mapped or the set$-$associative

cache better?