GATE CS 2016 Set 1 Q47 — Memory Management and Virtual Memory

To find the size of the per-process page table, we calculate the number of page table entries and multiply it by the size of each entry:

1. Determine the number of pages:
   Virtual Address size = $40\text{ bits}$
   Page size = $16\text{ KB} = 16 \times 2^{10}\text{ bytes} = 2^{14}\text{ bytes}$
   Number of pages in the virtual address space = $\frac{2^{40}}{2^{14}} = 2^{26}$
2. Determine the Page Table Entry (PTE) size:
   PTE size = $48\text{ bits} = \frac{48}{8}\text{ bytes} = 6\text{ bytes}$
3. Calculate the Page Table Size:
   Page Table Size = $\text{Number of pages} \times \text{PTE size}$
   Page Table Size = $2^{26} \times 6\text{ bytes}$
   Page Table Size in Megabytes (MB) = $\frac{2^{26} \times 6}{2^{20}}\text{ MB} = 2^6 \times 6\text{ MB} = 64 \times 6\text{ MB} = 384\text{ MB}$

Thus, the size of the per-process page table is 384 megabytes.