Calculating Page Table Size in Paging: Optimizing Virtual Memory Management

Learn how to calculate the size of a page table in a paging system. This tutorial explains the factors influencing page table size (page size, address space size), provides a step-by-step calculation method, and highlights the importance of optimizing page table size for efficient virtual memory management.

Calculating Page Table Size in Paging

Page Table Size and Memory Requirements

In paging, the operating system (OS) uses a page table to map virtual addresses (used by programs) to physical addresses (locations in RAM). The size of the page table is a crucial factor influencing performance because the page table itself needs to be accessed to translate virtual addresses. A large page table consumes significant memory and slows down memory access.

Calculating Page Table Size

The size of a page table depends on two factors:

  • The number of entries in the page table (equal to the number of pages in the process).
  • The size of each entry in the page table (typically 1 byte or more, depending on the number of bits needed to represent the frame number).

Let's calculate an example:

  • Logical address size: 24 bits
  • Page size: 4KB = 212 bytes

Number of bits for page offset (address within a page): 12 bits (log2(4KB) = 12)

Number of bits for page number: 24 - 12 = 12 bits

Number of pages: 212 = 4096 pages

Assuming each page table entry is 1 byte:

Page table size = Number of pages * Size of each entry = 4096 bytes = 4KB

In this case, the page table size is 4KB, conveniently fitting into a single 4KB frame. The CPU would keep the page table's base address in a register. To translate an address, the page number from the logical address would be added to the base address to get the frame number, which then provides the physical address by appending the page offset.

Handling Larger Page Tables

If the page table is larger than a single frame, it needs to be stored across multiple frames. This adds to the complexity of memory access and reduces the speed of address translation. Techniques like multi-level paging can help mitigate this, but introduce additional overhead.