Problem $3.(12$ points$)$ VIPT Cache

Consider a CPU with a memory system with the following parameters: Page size: $4$ KB

Cache capacity: $128$ KB

Cache set$-$associativity: $4$

Cache line size: $64$ bytes

A$.(3$ points$)$ How many copies of the same data can exist in the cache due to the synonym problem?

B$.(3$ points$)$ Is it possible to prevent synonyms through OS without changing the parameters of the memory system? If so$,$ how? If not, why can$$t it be done?

C$.(3$ points$)$ In order to prevent synonyms, consider changing the cache capacity. Assuming other design parameters remain the same, what should be the new cache size in KB$?$

D$.(3$ points$)$ Instead of changing the capacity, consider changing the page size and set$-$ associativity to prevent synonyms. If the page size is doubled, what should be the new set$-$ associativity $($i$.$e$.,$ how many ways are needed?$)$ Assume other parameters remain the same.