$($i$)$ A cache may be organized such that:

In one case, there are more data elements per block and fewer blocks

In another case, there are fewer elements per block but more blocks However, in both cases $-$

i$.$e$.,$ larger blocks but fewer of them OR shorter blocks, but more of them $-$ the cache's total

capacity $($amount of data storage$)$ remains the same

What are the pros and cons of each organization? Support your answer with a short example

assuming that the cache is direct mapped

$($ii$)$ Assume:

A processor has a direct mapped cache

Data words are $8$ bits long $($i$.$e$.,1$ byte$)$

Data addresses are to the word

A physical address is $20$ bits long

The tag is $11$ bits

Each block holds $16$ bytes of data

How many blocks are in this cache?

$($iii$)$ Consider a $16-$way set$-$associative cache:

Data words are $64$ bits long

Words are addressed to the half$-$word

The cache holds $2$ Mbytes of data

Each block holds $16$ data words

Physical addresses are $64$ bits long

How many bits of tag, index, and offset are needed to support references to this cache?