Problem $1.$ 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.

$254,187,45,182,15,191,89,192,3,44,181,4$

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.