$1.$To execute the following assembly code using a direct mapped cache with a larger block $($block size $\backslash (=4\backslash ))$ as shown in the figure.

What is the Hit$/$Miss rate?

$```$

li $tO$,5$

loop: beq $t$0,$ $$0,$ done

lw $t$1,0$x$4($$$0)$

lw $t$2,$OxC$($$$0)$

addi $to$,$ $to$,-1$

j loop

done:

$```$

$2.$ A cache has the following parameters: b block size given in numbers of words $\backslash (=1$ ; $\backslash$mathrm$\{$S$\}\backslash )$ number of sets $\backslash (=8$ ; $\backslash$mathrm$\{$N$\}\backslash )$ number of ways $\backslash (=2$ ; $\backslash )$ and A number of memory address bits $\backslash (=32\backslash ).$

$($a$)$ In terms of the parameters described, what is the cache capacity in numbers of words?

$($b$)$ In terms of the parameters described, what is the number of bits required to represent each tag?

$($c$)$ If $\backslash (\backslash$mathrm$\{$b$\}=2,\backslash$mathrm$\{$~S$\}=8,\backslash$mathrm$\{$~N$\}=1\backslash )($direct mapped cache$),\backslash (\backslash$mathrm$\{$A$\}=32\backslash ).$ What is the number of bits required to represent each tag?