A three-level page table translates 39-bit virtual addresses with fields: level-1 index 9 bits, level-2 index 9, level-3 index 9, page offset 12. Pages are 4 KB and every PTE is 8 bytes. A process uses 2 GB of virtual memory mapped to 2 GB physical memory. Find the minimum total page-table memory across all levels, in KB.
Two GB is 2³¹ bytes, hence 2³¹/2¹²=2¹⁹ mapped pages. Each leaf page-table block holds 4096/8=512=2⁹ entries, so 2¹⁰=1024 leaf blocks are needed. They require two level-two blocks, plus one root block. Total (1024+2+1)×4 KB=4108 KB. Contiguous aligned virtual allocation attains this minimum.
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