Assume a machine that has a 42-bit virtual address space, and a 32-bit physical address space (i.e., the maximum amount of physical memory for a 32-bit address space is present).

i. How many entries would you expect a single level page table to have when the page size is 4 kilobytes? Briefly explain your answer.

ii. How many entries would you expect to find in an inverted page table? Briefly explain your answer.

iii. Assuming that the memory access time is 90ns and the time it takes to search the translation lookaside buffer is 15ns. What is the average memory access time for a page table with 3 levels and a 98% hit rate (write down in equations how you get the result)?