$11)$ For these problems use a system with a page size of $4$K$,$ a virtual memory size of $32$GB$,$ and $2$MB of physical memory.

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a$)$ What is the size of the page table required to map a process with the above specifications?

b$)$ How much memory does a single frame worth of page table entries $$cover$?$

c$)$ Presume that a process has $64$ MB of code$/$data$/$heap and $88$MB of stack. How many frames for both page tables are required if the page table in question $11($a$)$ is allocated a second level page table?

d$)$ The memory system described in question $11($c$)$ has an $65$ns access time and utilizes a $5$ns cache. What is the average memory access time if the cache has a $80\%$ hit rate? Just the formula, with the appropriate values plugged in$,$ is sufficient