Problem $2[40$ pts$]$ : A memory system has $8$ KB byte$-$addressable main memory and a directmapped 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:

$\backslash$table$[[$$ Frame,Tag,Valid$],[000,10010,1],[001,10101,1],[010,01111,1],[011,10100,0],[100,01100,0],[101,10001,1]]$A memory system has $8$ KB byte$-$addressable main memory and a directmapped 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:

$\backslash$table$[[$$ Frame,Tag,Valid$],[000,10010,1],[001,10101,1],[010,01111,1],[011,10100,0],[100,01100,0],[101,10001,1]]$