A memory system has $8$ KB byte$-$addressable main memory and a direct$-$

mapped cache that consists of $8$ blocks with $32$ bytes per block. The following shows the main

memory address format that allows us to map addresses from main memory to cache.

Note: $13$ bit address, $5$ bit offset, $3$ bit cache frame #$,$ and $5$ bit tag

Assume the cache directory shown below:

$($The first three number are in $ frame second $5$ in tag and last number is for validation$)$

$Frame Tag Valid

$000100101$

$001101011$

$010011111$

$011101000$

$100011000$

$101100011$

$110000011$

$111111011$

Indicate whether each of the following memory references would result in a hit or a miss:

a$)0$x$0$A$35$

b$)0$x$1$EF$2$

c$)0$X$121$B

d$)0$x$0$C$97$