Now George P$.$ Burdell is studying the effect of set$-$associativity on the cache performance.

Since he now knows the access time of each configuration, he wants to know the miss$-$rate of

each one. For the miss$-$rate analysis, George is considering two small caches: a direct$-$mapped

cache with $8$ lines with $16$ bytes$/$line$,$ and a $4-$way set$-$associative cache of the same size. For the

set$-$associative cache, George tries out a least recently used $($LRU$)$ policy.

George tests the cache by accessing the following sequence of hexadecimal byte addresses,

starting with empty caches. For simplicity, assume that the addresses are only $12$ bits. Complete

the following tables for the direct$-$mapped cache and the LRU $4-$way set$-$associative cache

showing the progression of cache contents as accesses occur $($in the tables, 'inv' $=$ invalid, and

the column of a particular cache line contains the $\{$tag$,$index$\}$ contents of that line$).$ You only

need to fill in elements in the table when a value changes.