Structure of Page table

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Page Table Entries

page table entries are present in Page table in which each page table entry stores a frame number and other optional status bits (like protection) . Most of the status bits used in the virtual memory system. frame Number is the important thing in PTE .

Page table entry has the following information –


  1. Frame Number – It gives the frame number in which the current page you are looking for is present. The number of bits required depends on the number of frames.
    Number of bits for frame = Size of physical memory/frame size
  2. Present/Absent bit – Present or absent bit says whether a particular page you are looking for is present or absent. In case if it is not present, that is called Page Fault. It is set to 0 if the corresponding page is not in memory. Used to control page fault by the operating system to support virtual memory. Sometimes this bit is also known as valid/invalid bits.
  3. Protection bit – Protection bit says that what kind of protection you want on that page. So, these bit for the protection of the page frame (read, write etc).
  4. Referenced bit – Referenced bit will say whether this page has been referred in the last clock cycle or not. It is set to 1 by hardware when the page is accessed.
  5. Caching enabled/disabled – Some times we need the fresh data. Let us say the user is typing some information from the keyboard and your program should run according to the input given by the user. In that case, the information will come into the main memory. Therefore main memory contains the latest information which is typed by the user. Now if you try to put that page in the cache, that cache will show the old information. So whenever freshness is required, we don’t want to go for caching or many levels of the memory.The information present in the closest level to the CPU and the information present in the closest level to the user might be different. So we want the information has to be consistency, which means whatever information user has given, CPU should be able to see it as first as possible. That is the reason we want to disable caching. So, this bit enables or disable caching of the page.
  6. Modified bit – Modified bit says whether the page has been modified or not. Modified means sometimes you might try to write something on to the page. If a page is modified, then whenever you should replace that page with some other page, then the modified information should be kept on the hard disk or it has to be written back or it has to be saved back. It is set to 1 by hardware on write-access to page which is used to avoid writing when swapped out. Sometimes this modified bit is also called as the Dirty bit.

some of the most common techniques for structuring the page table.

Hierarchical Paging

Most modern computer systems support a large logical address space (232 to 264). In such an environment, the page table itself becomes excessively large. For example, consider a system with a 32-bit logical address space. If the page size in such a system is 4 KB (212), then a page table may consist of up to 1 million entries (232/212).

 Assuming that each entry consists of 4 bytes, each process may need up to 4 MB of physical address space for the page table alone. Clearly, we would not want to allocate the page table contiguously in main memory. One simple solution to this problem is to divide the page table into smaller pieces. We can accomplish this division in several ways. One way is to use a two-level paging algorithm, in which the page table itself is also paged (Figure 8.14). Remember our example of a 32-bit machine with a page size of 4 KB. A logical address is divided into a page number consisting of 20 bits and a page offset consisting of 12 bits. Because we page the page table, the page number is further divided into a 10-bit page number and a 10-bit page offset. Thus, a logical address is as follows:

Structure of Page table

Structure of Page table

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where p1 is an index into the outer page table and p2 is the displacement within the page of the outer page table. The address-translation method for this architecture is shown in Figure 8.15. Because address translation works from the outer page table inward, this scheme is also known as a forward-mapped page table. The VAX architecture also supports a variation of two-level paging. The VAX is a 32-bit machine with a page size of 512 bytes. The logical address space of a process is divided into four equal sections, each of which consists of 210 bytes. Each section represents a different part of the logical address space of a process. The first 2 high-order bits of the logical address designate the appropriate section. The next 21 bits represent the logical page number of that section, and the final 9 bits represent an offset in the desired page. By partitioning the page

Structure of Page table

table in this manner, the operating system can leave partitions unused until a process needs them. An address on the VAX architecture is as follows:

Structure of Page table

where s designates the section number, p is an index into the page table, and d is the displacement within the page. Even when this scheme is used, the size of a one-level page table for a VAX process using one section is 221 bits + 4 bytes per entry = 8 MB. So that main-memory use is reduced further, the VAX pages the user-process page tables. For a system with a 64-bit logical-address space, a two-level paging scheme is no longer appropriate. To illustrate this point, let us suppose that the page size in such a system, is 4 KB (212). In this case, the page table consists of up to 252 entries. If we use a two-level paging scheme, then the inner page tables can conveniently be one page long, or contain 210 4-byte entries. The addresses look like this:

Structure of Page table

The outer page table consists of 2 entries, or 2 bytes. The obvious way to avoid such a large table is to divide the outer page table into smaller pieces. This approach is also used on some 32-bit processors for added flexibility and efficiency.
We can divide the outer page table in various ways. We can page the outer page table, giving us a three-level paging scheme. Suppose that the outer page table is made up of standard-size pages (210 entries, or 212 bytes); a 64-bit address space is still daunting:

Structure of Page table

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The outer page table is still 234 bytes in size.

The next step would, be a four-level paging scheme, where the secondlevel outer page table itself is also paged. The SPARC architecture (with 32-bit addressing) supports a three-level paging scheme, whereas the 32-bit Motorola 68030 architecture supports a four-level paging scheme. For 64-bit architectures, hierarchical page tables are generally considered inappropriate. For example, the 64-bit UltraSPARC would require seven levels of paging—a prohibitive number of memory accesses—to translate each logical address.

Hashed Page Tables

 A common approach for handling address spaces larger than 32 bits is to use a hashed page table, with the hash value being the virtual page number. Each entry in the hash table contains a linked list of elements that hash to the same location (to handle collisions). Each element consists of three fields: (1) the virtual page number, (2) the value of the mapped page frame, and (3) a pointer to the next element in the linked list. The algorithm works as follows:

The virtual page number in the virtual address is hashed into the hash table. The virtual page number is compared with field 1 in the first element in the linked list. If there is a match, the corresponding page frame (field 2) is used to form the desired physical address.

Structure of Page table

Structure of Page table

If there is no match, subsequent entries in the linked list are searched for a matching virtual page number. This scheme is shown in Figure 8.16. A variation of this scheme that is favorable for 64-bit address spaces has been proposed. This variation uses clustered page tables, which are similar to hashed page tables except that each entry in the hash table refers to several pages (such as 16) rather than a single page. Therefore, a single page-table entry can store the mappings for multiple physical-page frames. Clustered page tables are particularly useful for sparse address spaces, where memory references are noncontiguous and scattered throughout the address space.

 Inverted Page Tables

Usually, each process has an associated page table. The page table has one entry for each page that the process is using (or one slot for each virtual address, regardless of the latter's validity). This table representation is a natural one, since processes reference pages through the pages' virtual addresses. The operating system must then translate this reference into a physical memory address. Since the table is sorted by virtual address, the operating system is able to calculate where in the table the associated physical address entry is and to use that value directly.

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One of the drawbacks of this method is that each page table may consist of millions of entries. These tables may consume large amounts of physical memory just to keep track of how other physical memory is being used. To solve this problem, we can. use an inverted page table. An inverted page table has one entry for each real page (or frame) of memory.

Each entry consists of the virtual address of the page stored in that real memory location, with information about the process that owns that page. Thus, only one page table is in the system, and it has only one entry for each page of physical memory. Figure 8.17 shows the operation of an inverted page table. Inverted page tables often require that an address-space identifier be stored in each entry of the page table, since the table usually contains several different address spaces mapping physical memory.

Storing the address-space identifier ensures that a logical page for a particular process is mapped to the corresponding physical page frame. Examples of systems using inverted page tables include the 64-bit UltraSPARC and PowerPC.

To illustrate this method, we describe a simplified version of the inverted page table used in the IBM RT. Each virtual address in the system consists of a triple .


Each inverted page-table entry is a pair where the process-id assumes the role of the address-space identifier. When a memory reference occurs, part of the virtual address, consisting of , “,” is presented to the memory subsystem. The inverted page table is then searched for a match. If a match is found—say; at entry i—then the physical address.

” is generated. If no match is found, then an illegal address access has been attempted.

Although this scheme decreases the amount of memory needed to store each page table, it increases the amount of time needed to search the table when a page reference occurs. Because the inverted page table is sorted by physical address, but lookups occur on virtual addresses, the whole table might need to be searched for a match. This search would take far too long. To alleviate this problem, we use a hash table, to limit the search to one—or at most a few—page-table entries. Of course, each access to the hash table adds a memory reference to the procedure, so one virtual memory reference requires at least two real memory reads—one for the hash-table entry and one for the page table.

To improve performance, recall that the TLB is searched first, before the hash table is consulted. Systems that use inverted page tables have difficulty implementing shared memory. Shared memory is usually implemented as multiple virtual addresses (one for each process sharing the memory) that are mapped to one physical address. This standard method cannot be used with inverted page tables; because there is only one virtual page entry for every physical page, one physical page cannot have two (or more) shared virtual addresses. A simple technique for addressing this issue is to allow the page table to contain only one mapping of a virtual address to the shared physical address. This means that references to virtual addresses that are not mapped result in page faults.

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