A byte$-$addressable main memory of size $64$MB with blocks of size $64$B$.$ The cache memory has $256$ blocks $($ the block is also of size $64$B$)$ in addition to the space for tag and validity bit.

For each of the following cache organization, determine the number of bits of Byte Offset, Tag, and index $($block number in cache for direct Mapped organization$)$ and the set $($ number in the $2-$way set associative$),$ and fully associative.

For each one of the three organizations, determine whether each of the following memory addresses is a hit or a miss.

$2,16,210+7,212+28,212+7,63,210+12,210,215+1,4$

Assume the cache blocks initially are not used.

Create a table for each organization and show the cache content after each above reference and indicate whether the reference is a hit or a miss.