$(4)3$ M decides to make Post$-$its by printing yellow squares on white pieces of paper. As part of the printing process, they need to set the CMYK $($cyan$,$ magenta, yellow, black$)$ value for every point in the square. $3$M hires you to determine the efficiency of the following algorithms on a machine with a $2,048-$byte direct$-$mapped data cache with $32-$byte blocks. You are given the following definitions:

$```$

struct point$\_$color $\{$

int c;

int m;

int y;

int k;

$\}$;

struct point$\_$color square$[16][16]$;

int i$,$ j;

$```$

Assume the two functions are executed under the following conditions:

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

$-$ square begins at memory address $0.$

$-$ The cache is initially empty.

$-$ The only memory accesses are to the entries of the array square. Variables $\backslash ($ i $\backslash )$ and $\backslash ($ j $\backslash )$ are stored in registers.

$```$

A$.[1+4+1]$

for $($i $=0$; i $<mtext></mtext><mn>1</mn><mn>6</mn>$; i$++)\{$

for $($j $=0$; j $<mtext></mtext><mn>1</mn><mn>6</mn>$; j$++)\{$

square$[$i$][$j$].$c $=0$;

square$[$i$][$j$].$m $=0$;

square$[$i$][$j$].$y $=1$;

square$[$i$][$j$].$k $=0$;

$\}$

$8\}$

$```$

$($a$)$ What is the total number of writes? Explain.

$($b$)$ What is the total number of writes that miss in the cache? Explain.

$($c$)$ What is the miss rate? Explain.