$2.$ As a cache plays an important role to provide high$-$performance memory hierarchy to processors. Below is a list of $32-$bit memory addresses. Note that all reference addresses are word addresses.

$3,2,11,180,190,15,191,72,186,77$

a$.$ Given a direct$-$mapped cache containing $16$ one$-$word$-$size blocks. For each of these references, identify the binary address, the tag, and the index. Also list if each reference is a hit or a miss, assuming the cache is initially empty. $(10$ pts$)$

b$.$ Suppose that the direct$-$mapped cache setting is changed to $8$ four$-$word$-$size blocks. For each of these references, identify the binary address, the tag, and the index given a direct$-$mapped cache. Also list if each reference is a hit or a miss, assuming the cache is initially empty. $(10$ pts$)$