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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?

  1. $6$
  2. None of the above
  3. $7$
  4. $5$
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