Q$4)(4$ Points$)$ Memory Management

Consider a logical address space of $2,048$ pages with a $4-$KB page size, mapped onto a physical memory of $512$ frames.

Assuming a paged memory:

a$)(1$ Point$)$ How many bits are required in the logical address?

b$)(1$ Point$)$ How many bits are required in the physical address?

c$)(1$ Point$)$ Assume the page tables are stored in memory. If a memory reference takes $50$ nanoseconds, how long does a paged memory reference take?

d$)(1$ Point$)$ If we add TLBs$,$ and if $75$ percent of all page$-$table references are found in the TLBs$,$ what is the effective memory reference time? $($Assume that finding a page$-$table entry in the TLBs takes $2$ nanoseconds, if the entry is present.$)$

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