Consider a computer architecture that has a dynamically changing caching policy, such that it changes

either the block size or the associativity of the caching policy in the middle of execution. In some cases,

the change may require the computer to invalidate existing blocks in the cache because the blocks stored

under the old caching policy are either misplaced or incomplete according to the new policy. For each

case below, indicate whether the change may lead to blocks in the cache that are no longer valid, or if all

blocks that were in the cache before the change remain valid after the change.

$($a$)$ Direct$-$mapped: block size doubles from $16$ words $/$ block to $32$ words $/$ block

$($b$)$ Direct$-$mapped: block size halves from $16$ words $/$ block to $8$ words $/$ block

$($c$)$ Fully assoc: block size doubles from $16$ words $/$ block to $32$ words $/$ block

$($d$)$ Fully assoc: block size halves from $16$ words $/$ block to $8$ words $/$ block

$($e$)$ Set assoc, goes from $4-$way to $8-$way associative

$($f$)$ Set assoc, goes from $4-$way to $2-$way associative