It's $1987$ and Apple has just released the Macintosh II featuring a Motorola $68030$ processor. The $68030$ contains a state of the art $128$ byte data$-$cache and uses byte$-$addressable memory. Having taken $370,$ you know there's more to cache design than just size, so you write a C program to help you determine the block size, number of blocks per set, and number of sets in the cache. You have a function ACCESS$($char $*)$ that loads the memory at the given pointer. Assume all variables other than the data$[]$ array are stored in registers and that the cache has been cleared before each call to miss$\_$rate$(...).$ Assume data$[0]$ is at the start of the cache block.

$```$

#define CACHE$\_$SIZE XX

double miss$\_$rate$($int stride$)\{$

char data$[$CACHE$\_$SIZE $*2]$; $//$ note array is $2*$cache size

for $($int i $=0$; i $$ stride; i$++)\{$

for $($int j $=$ i; j $<mtext></mtext><mi>(</mi>$CACHE$\_$SIZE $*2)$; j $+=$ stride$)\{$

ACCESS$($data $+$ j$)$

$\}$

$\}$

$\}$

$```$

$1.$ In order to test your code, you first run it on a $256$ B fully$-$associative cache with $32$ B blocks. You set the CACHE$\_$SIZE macro to $256.$ Fill in the miss rate for each stride in the following table. Only answers in the table will be graded. Fractions are OK$.[6]$ You now run your program on the Motorola $68030$ processor with a $128$ byte data$-$cache. You set the CACHE$\_$SIZE macro to $128$ and collect the following data

Using the above data answer the following questions and justify your answers.

$2.$ What is the block size in bytes? $[3]$

$3.$ What is the associativity of the cache? $[3]$

$4.$ How many sets are there in the cache? $[3]$