$2-$Caches are important to providing a high$-$performance memory hierarchy to

processors. Below is a list of $32-$bit memory address references, given as word

addresses.

a$.$ For each of these references, identify the binary address, the tag, and the index given a direct$-$mapped cache with two$-$word blocks and a total size of

$4$ blocks. Also list if each reference is a hit or a miss, assuming the cache is

initially empty.

$42,170,46,175,178,6,174,41,5,180,65,181$

b$.$ For each of these references, identify the binary address, the tag, and the index given a direct$-$mapped cache with four$-$word blocks and a total size

of $4$ blocks. Also list if each reference is a hit or a miss, assuming the cache

is initially empty.