$1.$ Cache Performance $[15$ points$]$

Our embedded system has an $8$KB direct$-$mapped data cache with $8-$byte blocks. The cache is using write$-$back and write allocate policy. The cache is initially empty before executing the following code.

For $($i$=0$;i$<3$;i$++)$

For $($j$=0$;j$<100$;j$++)$

A$[$i$][$j$]=$ B$[$j$][0]+$B$[$j$+1][0]$;

The array A and B contain $4-$byte elements. The array A has $3$ rows and $100$ columns. The array B has $101$ rows and $3$ columns. The layout for the array A is as follows. The array B has a similar layout.

Memory layout for array A$.$

A$[0][0]$ A$[0][1]$ A$[0][2]$ A$[0][3]$ A$[0][4]$

$...$

$($a$)[5$ points$]$ How many times does the array A cause cache misses when we running above code?

$($b$)[5$ points$]$ How many times does the array B cause cache misses when we executing above code? What type of locality do the accesses for the array B has?

$($c$)[5$ points$]$ What$$s the total miss rate when we execute above code assuming cache is sufficiently big to contain array A and B$?$