A two$-$way set$-$associative cache in a system with $32-$bit addresses has four $4-$byte words per line and a capacity of $1$ MB$.$ Addressing is to the byte level.

$($a$)$ How many bits are there in the index and the tag?

$($b$)$ Indicate the value of the index in hexadecimal for cache entries from the following main memory addresses in hexadecimal: $00$F$8$C$00$F$,4214$AC$89,7142$CF$0$F$,2$BD$4$CF$0$C$,$ and F$83$ACF$04.$

$($c$)$ Can all of the cache entries from part $($b$)$ be in the cache simultaneously?