$(15$ Points$)$ Cache Design

A certain processor has a physical address of $30$ bits $($therefore the total memory size is $2$ bytes and is byte addressable$).$ The cache size is $250$ Kbytes with a block size of $16$ bytes.

$($Note: Everything here is in bytes and not words$).$

$1.(5$ Points$)$ For a direct mapping, how many bits is the tag field, the index field, and the block offset field $($the bits identifying a byte within a block$).$

$2.(5$ Points$)$ For a $8-$way set associative mapping, how many bits is the tag field, the index field, and the block offset field.

$3.(5$ Points$)$ For a fully associative mapping, how many bits is the tag field, the index field, and the block offset