Paging Calculator
A single-level page table has one entry per virtual page: 32-bit addresses with 4 KB pages and 4-byte entries need 4194304 bytes, 4 MB.
4194304 bytes
- Page offset bits
- 12
- Virtual page number bits
- 20
- Number of pages
- 1048576
- Frame number bits
- 18
- Number of frames
- 262144
- Page table size
- 4 MB
- Levels needed so each table fits in one page
- 2
- Effective access time with TLB
- 120 ns
- Without TLB (2 memory accesses)
- 200 ns
Step-by-step solution
- Offset = log₂(4096) = 12 bits
- Pages = 2^(32 − 12) = 1048576; table size = pages × PTE = 4194304 bytes
- EAT = h(t_TLB + tₘ) + (1 − h)(t_TLB + 2tₘ) = 120 ns
Paging Formula
page table size = 2^(VA − offset) × PTE
EAT = h(t + m) + (1 − h)(t + 2m)
Worked Example
A 32-bit virtual address, 4 KB pages and 4-byte page table entries:
- Offset = log₂(4096) = 12 bits
- Pages = 2^(32 − 12) = 1048576; table size = pages × PTE = 4194304 bytes
- EAT = h(t_TLB + tₘ) + (1 − h)(t_TLB + 2tₘ) = 120 ns
Virtual page number bits: 20 · Number of pages: 1048576 · Frame number bits: 18 · Number of frames: 262144 · Page table size: 4 MB · Levels needed so each table fits in one page: 2 · Effective access time with TLB: 120 ns · Without TLB (2 memory accesses): 200 ns
GATE tip
For multi-level paging, each level indexes as many bits as fit one page of entries: log₂(page size ÷ PTE). The “levels needed” row does this division for you.
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Frequently asked questions
Why use multi-level page tables?
A single-level table for a large address space is huge and mostly empty; splitting it lets unused regions have no tables at all.
How does a TLB reduce access time?
A TLB hit avoids the page-table memory access, so effective access time approaches one memory access as the hit ratio rises.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Paging Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/paging-calculator/
IEEE
Scientific Converters, "Paging Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/paging-calculator/