Consider a computer system with $32-$ bit virtual addressing and page size of sixty-four kilobytes. The computer system has one-level page table per process with each page table entry of $6$ bytes. If the maximum physical memory size supported by this paging system is given to be $128$ petabytes $(2^{57}\; \text{bytes}),$ how many bits can be used for flags and permissions within a page table entry?
- $6$
- None of the above
- $7$
- $5$
