A byte$-$addressable main memory of size $4096$ MB with blocks of $32$ bytes in size. The cache memory can hold up to $512$ blocks of data in addition to the space for tag and validity bit. Show the fields in a memory address $($the name of each part and its length in bits$)$ and the actual size of cache memory in bits $($i$.$e$.$ the storage for data plus tags and validity bits$)$ for each of the following organizations.

Full Associative

Direct$-$mapping

$2-$way set associative

For each of the three above cache memory organizations, compute the offset, index, or set, and tag for the address.

$2^24+2^6+7$