$3)(30$ pts$)$ In a hypothetical system with $256$ bytes of main memory, $64$ bytes of cache, blocks of $8-$byte size, a $2-$way associative placement policy and an LRU replacement policy for each set, determine, for each block in cache,

$($a$)$ the block address $($in decimal representation$)$ of the memory block stored in it$,$ and

$($b$)$ the content of the age register $($priority counter$)$ of it$,$ at the end of each memory access shown in the following address sequence generated by CPU $($a very unlikely case, of course$).$

x$4$b x$3$f x$36$ x$6$d x$24$ x$54$ x$70$ x$4$d x$8$a x$56$ x$90$ x$40$ xae x$4$f x$9$a

Also determine the hit ratio from this sequence of accesses.

Note: in order to start finding the location to place into an empty set in cache, make sure that age registers of all blocks in each set are properly initialized; e$.$g$.,$ a $2-$way set would have the $2$ counters initialized as $0$ and $1,$ whereas a $4-$way set would have the $4$ counters initialized as $0,12$ and $3,$ and so on$.$ Hint: the first address x $4$ b would have its block address equal to $"9"$ in decimal value to be placed into your target cache block in your solution.

Below is an example showing a cache of two sets with $4$ blocks each $($i$.$e$.,\backslash ($ S$=4\backslash ))$ and the format of information you need to provide in your solution $($note: this is not conforming to the parameters for this problem$).$ In this hypothetical example, the block that contains the first access with address x$39$ is found to have a block address of $17$ and is placed into set $0.$