Logical address space of a process can be noncontiguous; process is  allocated physical memory 

whenever the latter is available.

Divide physical memory into fixed-sized blocks called frames (size is power of 2, between  512 bytes and 8192 bytes).   

Divide logical memory into blocks of same size called pages.

Keep track of all free frames.

To run a program of size n pages, need to find n free frames and load program.

Set up a page table to translate logical to physical addresses.   

Internal fragmentation.


Address Translation Scheme


Address generated by CPU is divided into:

   1.  Page number (p) – used as an index into a page table which contains base address of each page

                                            in physical memory.

   2.  Page offset     (d) – combined with base address to define the physical memory address that is 

                                             sent to the memory unit.


Address Translation Architecture




Paging Example




Paging Example




Free Frames




Before allocation After allocation


Implementation of Page Table


Page table is kept in main memory.

Page-table base register (PTBR) points to the page table.

Page-table length register (PRLR) indicates size of the page table.

In this scheme every data/instruction access requires two memory accesses. One for the page table and one for the data/instruction.

The two memory access problem can be solved by the use of a special

fast-lookup hardware cache called associative memory or translation look-aside buffers (TLBs)


Associative Memory


Associative memory – parallel search Address translation (A´, A´´)

  1. If A´ is in associative register, get frame # out.

  2. Otherwise get frame # from page table in memory

                 Page #                                                       Frame #











Paging Hardware With TLB




Effective Access Time


Associative Lookup = å time unit

Assume memory cycle time is 1 microsecond

Hit ratio – percentage of times that a page number is found in the associative registers; ration related to

                   number of associative registers.

Hit ratio = a

Effective Access Time (EAT)

EAT = (1 + å) a + (2 + å)(1 – a)

         = 2 + å – a

Memory Protection


Memory protection implemented by associating protection bit with each frame.

Valid-invalid bit attached to each entry in the page table:

  1. “valid” indicates that the associated page is in the process’  logical address space, and is thus a  

         legal page.

  2. “invalid” indicates that the page is not in the process’ logical  address space.


Valid (v) or Invalid (i) Bit In A Page Table



Page Table Structure


  1.  Hierarchical Paging

  2.  Hashed Page Tables

  3. Inverted Page Tables


Hierarchical Page Tables


Break up the logical address space into multiple page tables.

A simple technique is a two-level page table.


Two-Level Paging Example


A logical address (on 32-bit machine with 4K page size) is divided into:

   1. a page number consisting of 20 bits.

   2. a page offset consisting of 12 bits.

Since the page table is paged, the page number is further  divided into:

  3. a 10-bit page number.

  4. a 10-bit page offset.

  5. Thus, a logical address is as follows:

                   page number                                                   page offset

       pi                          p2                                   d






    10                     10                                              12


where pi is an index into the outer page table, and p2 is the  displacement within the page of the outer page table.


Two-Level Page-Table Scheme




Address-Translation Scheme


Address-translation scheme for a two-level 32-bit paging  architecture




Hashed Page Tables


Common in address spaces > 32 bits.

The virtual page number is hashed into a page table. This page table contains a chain of elements hashing to the same location.

Virtual page numbers are compared in this chain searching for a match. If a match is found, the

corresponding physical frame is extracted.


Hashed Page Table




Inverted Page Table


One entry for each real page of memory.

Entry consists of the virtual address of the page stored in that real memory location, with information about the process that owns that page.

Decreases memory needed to store each page table, but  increases time needed to search the table when a page reference occurs.

Use hash table to limit the search to one — or at most a  few — page-table entries.


Inverted Page Table Architecture




Shared Pages


Shared code

    1. One copy of read-only (reentrant) code shared among processes (i.e., text editors, compilers,

         window systems).

    2. Shared code must appear in same location in the logical  address space of all processes.

         Private code and data

    3. Each process keeps a separate copy of the code and data.

                   4. The pages for the private code and data can appear

                        anywhere in the logical address space.


Shared Pages Example