Main Memory Access Time: $100$ ns

Cache Access Time: $10$ ns

Cache Hit Rate: $90\%$

Cache Block Size: $64$ bytes

Cache Associativity: $4-$way set associative

Main Memory Block Transfer Time: $500$ ns

Assume that the cache uses the LRU $($Least Recently Used$)$ replacement policy.

a$)$ Calculate the average memory access time for this system.

b$)$ Determine the effective access time if the cache hit rate is improved to $95\%$ while keeping all other parameters constant.

c$)$ If the cache size is doubled while maintaining the same cache associativity, calculate the new average memory access time assuming the cache hit rate remains at $90\%.$