Problem $2[40$ pts$]$ : A memory system has $4$ KB byte$-$addressable main memory and a directmapped cache that consists of $8$ frames with $16$ bytes per frame. The following shows the main memory address format that allows us to map addresses from main memory to cache. Note: $12$ bit address, $4$ bit offset, $3$ bit $Frame, and $5$ bit tag

Assume the cache directory shown below:

$\backslash$table$[[$Block$,$Tag,valid$],[000,10010,1],[001,10101,1],[010,01111,1],[011,10100,0],[100,11101,1],[101,10001,1],[110,00001,1],[111,11101,0],[,,]]$

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

a$)$ OX$8$DF

b$)$ OxE$65$

c$)$ OXEF$2$

d$)$ OXA$9$B