consider a machine with 64Mbyte physical memory and a 32 bit virtual address.…

Determine the Number of Pages (Entries in Page Table)

The number of entries in a single-level page table is equal to the number of virtual pages in the virtual address space.

• Virtual Address Space: 232 bytes (since it is a 32-bit address).

• Page Size: 4kB = 212 bytes.

• Number of Entries: 232/212 = 220 entries (approx. 1 million entries).

2. Determine the Page Table Entry (PTE) Size

A Page Table Entry must, at minimum, store the physical frame number.

• Physical Memory: 4MB = 226 bytes.

• Number of Frames: 226 / 212 = 214 frames.

• To address 214 frames, we need 14 bits.

• In practice, PTEs also include protection bits (valid/invalid, read/write, dirty bits). Typically, PTE sizes are rounded up to the nearest byte or power of 2 for alignment. A 14-bit address would require at least a 2-byte (16-bit) entry.

3. Calculate Total Page Table Size

Total Size = Number of Entries x PTE Size

Total Size = 220 x 2 bytes = 2 x 220 bytes = 2 Mbyte