$1.$ A byte$-$addressed machine with a word size of $16$ bits and address width of $32$ bits has a direct$-$mapped cache with $16$ blocks and a block size of $2$ words.

$($a$)$ Given a sequence of memory references as shown below, where each reference is given as a byte address in both decimal and hexadecimal forms, indicate whether the reference is a hit $($H$)$ or a miss $($M$).$ For a miss, also identify the type of miss it is $($i$.$e$.,$ cold, conflict or capacity.$)$ Assume that the cache is initially empty.

$($b$)$ Given the above sequence of memory references, fill in the final contents of the cache. Use the notation $\backslash ($ M$[$i$]\backslash )$ to denote the word at memory address $\backslash ($ i $\backslash ).$