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Page fault; virtual to physical address

Short answer

A page fault occurs when a referenced page is not in main memory. For virtual address 20482 with 4KB pages, page number is 5, offset 2; given page table maps page 5 to frame 3, so physical address is 12290 (no fault).

What is page fault? Assume that a virtual memory of size 64K is mapped to physical memory of 32K with page frame 4K. Initially, pages are mapped as: 0,1,2,3,4,5,9,11 correspond to 2,1,6,0,4,3,5,7 respectively. Calculate outgoing physical address for incoming virtual address 20482 with necessary mapping diagrams.

Page fault

A page fault is a trap raised by the MMU when a process references a page that is in its virtual address space but whose page-table entry is marked not present in main memory. The OS then finds the page on disk, loads it into a free frame (replacing a page if none is free), updates the page table and restarts the instruction.

Address translation

  • Page size = frame size = 4 KB = 4096 bytes.
  • Virtual pages = 64K / 4K = 16 (pages 0 to 15, 4-bit page number); physical frames = 32K / 4K = 8 (frames 0 to 7, 3-bit frame number). Offset = 12 bits.
  • Virtual address = 20482. Page number = 20482 div 4096 = 5 (5 × 4096 = 20480). Offset = 20482 − 20480 = 2.

Page table (given mappings; others not present):

 page : 0 1 2 3 4 5 9 11
 frame: 2 1 6 0 4 3 5 7

Page 5 maps to frame 3 (present, so no page fault).

 Virtual address 20482 = 0101 000000000010
                          |        |
                      page 5     offset 2
                          v
                 page table[5] = frame 3 (011)
                          v
 Physical address = 011 000000000010
                  = 3 x 4096 + 2 = 12290

Answer: physical address = 12290 (frame 3, offset 2; hexadecimal 0x3002).

✓ Answer checked by Claude Opus 5.5 (high effort)

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