Cache Performance Comparison

$$ Cache size: $64$ KB

$$ Cache block size: $32$ bytes

$$ Cache access time: $2$ nanoseconds

$$ Memory access time: $50$ nanoseconds

$$ The system cache is direct$-$mapped, and the CPU generates $32-$bit memory addresses.

$$ The cache has a hit ratio of $85\%.$

The CPU reads $10$ MB of data from memory in a random access pattern, first checking the cache. If the data is

not found in the cache, it is retrieved from memory.

$1.$ Calculate the total time required to read the data with the given hit ratio.

$2.$ Determine the time required to read the same data without using the cache.

$3.$ Compare the performance with and without the cache. Express the improvement as a percentage