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: