$(3)[4+2+4+2+2]$ You are given the following code to analyze:

$1.$ int x$[2][128]$;

$2.$ int i$,$ sum $=0$;

$3.$ for $($i $=0$; i $<128$; i$++)$

$4.$ sum $+=$ x$[0][$i$]*$ x$[1][$i$]$;

Assume the code is executed under the following conditions:

$$ sizeof$($int$)=4$

$$ Array x begins at mem. addr. $0$x$0$ and is stored in row$-$major order.

$$ Cache initially empty

$$ Only mem. accesses are to elements of x$.$ Rest of the variables are in

registers.

$($a$)$ Case $1$: Assume cache is $512$ bytes, direct$-$mapped, with $16$ byte blocks.

What is the miss rate? Explain.

$($b$)$ Case $2$: What is the miss rate if the cache size is doubled $($becomes $1024$

bytes$).$ Explain.

$($c$)$ Case $3$: If the cache were to be a $512$ byte, two$-$way set$-$associative cache

using an LRU replacement policy, with $16$ byte cache blocks. What is

the cache miss rate? Explain.

$($d$)$ For case $3,$ will a larger cache size help reduce the miss rate? Why or

why not?

$($e$)$ For case $3,$ will a larger block size help reduce the miss rate? Why or

why not?