$($i$)$How many total bits$($include whatever is necessary for cache to work$)$ are required for a $8$ way set associative cache with $4$ MB of data and $8$ word block size assuming a $32$ bit address? Assume $1$ word is $4$ bytes and cache uses write back policy

$($ii$)$ Assume a memory system with cache with $1$MB $4$ way set associative cache as L$1$ cache and $4$ MB $8$ way set associative cache as $12$ cache. The hit time of L$1$ id given as $2$ cycles GMR of L$1$ is $4\%$ hit time of L$2$ is $8$ cycles, GMR of L$2$ is $2\%$ and miss penalty of L$2$ is $80$ cycles. Calculate the AMAT of thr memory system

$($iii$)$ The branch outcome of one branch instruction was $($NT$,$ T$,$ T$,$ NT$,$ NT$,$ T$)$ what are the accuries of the following branch predictors on branch instruction $?$

a$)(0,1)$ correlating predictor with all entries initialized to token

b$)(2,1)$ correlating predictor with all entries initialized to token