Problem 1 Consider a 64-bit, byte-addressable system that uses virtual memory. The system has 32GB of physical memory installed with a page size of 4KB. a) How many bits are used for the page offset? How many bits are used to index into the page table(s)? Page Offset: Virtual Page Number Bits: b) How many virtual pages exist in the system? c) How many physical pages exist in the system? d) If the system has a single-level page table with 4B entries, how large must the page table be to map all the system's virtual memory? If we switch to a hierarchical page table such that each page table level must fit in a single page, how many page table levels would we need to map all of the system's virtual memory? Assume page table entries are still 4B each. e)