$1.$Describe how multilevel caching can improve cache performance.

$2.$Explain the difference between read$-$stall cycles and write$-$stall cycles in cache performance.

$3.$Discuss the trade$-$offs between a direct$-$mapped cache and a fully associative cache.

$4.$Describe the role of a page table in a virtual memory system.

$5.$Explain how virtual memory systems handle page faults and the role of the operating system in this process.

$6.$Calculate the average memory access time $($AMAT$)$ for a processor with a $2$ ns clock cycle, a miss penalty of $50$ clock cycles, a miss rate of $0\mathrm{.}03,$ and a cache access time of $1$ clock cycle.

$7.$Consider a web service that aims to achieve $99\mathrm{.}99\%$ availability. Based on the shorthand of "nines of availability," calculate the maximum allowable downtime per year. Propose strategies to minimize downtime, focusing on reducing MTTR and improving MTTF$.$

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