$(12$ points$)$ 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.

$4,180,43,2,191,88,190,14,181,44,186,253$

$2\mathrm{.}1-$ For each of these references, identify the binary address, the tag, and the index

given a direct$-$mapped cache with $16$ one$-$word blocks. Also list if each reference is a hit

or a miss, assuming the cache is initially empty. $(6$ points$)$

$2\mathrm{.}2-$ 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 $8$ blocks. Also list

if each reference is a hit or a miss, assuming the cache is initially empty. $(6$ points$)$