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.