# Paging in Operating System

• Difficulty Level : Medium
• Last Updated : 21 Sep, 2021

Paging is a memory management scheme that eliminates the need for contiguous allocation of physical memory. This scheme permits the physical address space of a process to be non – contiguous.

• Logical Address Space or Virtual Address Space( represented in words or bytes): The set of all logical addresses generated by a program
• Physical Address (represented in bits): An address actually available on memory unit
• Physical Address Space (represented in words or bytes): The set of all physical addresses corresponding to the logical addresses

Example:

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• If Logical Address = 31 bit, then Logical Address Space = 231 words = 2 G words (1 G = 230)
• If Logical Address Space = 128 M words = 27 * 220 words, then Logical Address = log2 227 = 27 bits
• If Physical Address = 22 bit, then Physical Address Space = 222 words = 4 M words (1 M = 220)
• If Physical Address Space = 16 M words = 24 * 220 words, then Physical Address = log2 224 = 24 bits

The mapping from virtual to physical address is done by the memory management unit (MMU) which is a hardware device and this mapping is known as paging technique.

• The Physical Address Space is conceptually divided into a number of fixed-size blocks, called frames.
• The Logical address Space is also splitted into fixed-size blocks, called pages.
• Page Size = Frame Size

Let us consider an example:

• Physical Address = 12 bits, then Physical Address Space = 4 K words
• Logical Address = 13 bits, then Logical Address Space = 8 K words
• Page size = frame size = 1 K words (assumption) Address generated by CPU is divided into

• Page number(p): Number of bits required to represent the pages in Logical Address Space or Page number
• Page offset(d): Number of bits required to represent particular word in a page or page size of Logical Address Space or word number of a page or page offset.