The size of the page table in the system in megabytes is _____. Physical Address (20-bit address)= Segment * 10h + Offset. Since, the given memory has size of 16 GB, so we have-. (from 100 to 140 nanoseconds). The main memory is byte addressable. Thus, Number of bits in physical address = 26 bits, Thus, Number of bits in frame number = 14 bits, Thus, Number of bits in page offset = 12 bits, Number of bits in virtual address space = 32 bits, Thus, Number of entries in page table = 220 entries, = Number of entries in page table x Number of bits in frame number, = 220 x 16 bits      (Approximating 14 bits ≈ 16 bits). Calculate the size of memory if its address consists of 22 bits and the memory is 2-byte addressable. Physical Address Space = Size of main memory, Size of main memory = Total number of frames x Page size, Number of pages the process is divided = Process size / Page size, Size of page table = Number of entries in page table x Page table entry size, Number of entries in pages table = Number of pages the process is divided, Page table entry size = Number of bits in frame number + Number of bits used for optional fields if any, In general, if the given address consists of ‘n’ bits, then using ‘n’ bits, 2. Assuming the same here, since the offset is 4 bits and since the pages size has to be the same as the frame size = 2^4 = 16 bytes. The following list of formulas is very useful for solving the numerical problems based on paging. Then, Size of memory = 2n x 4 bytes. A larger page size means more waste when a page is partially used, so the system runs out of memory sooner. associative looks at all the entries at the same time, only a few page number/frame number pairs can be stored at once, stores the entries from the most recently used pages, when a process tries to access an address Calculate the size of memory if its address consists of 22 bits and the memory is 2-byte addressable. Practice Problems based on Paging and Page Table in OS. Most systems assume the lowest common addressable denomination is 1 byte. (based on PFF). then the the last 12 bits give the page offset, and Address: can be an address of an instruction, or of data This means only 1/2 the physical memory is addressable at any given instant. Assume the memory is 4-byte addressable. With the number of associative registers ranging between 16 and 512, a hit Page table performs the mapping of page number to frame number. Paging in OS | Formulas | Practice Problems. Number of bits in logical address = 32 bits, Number of entries in page table = 220 entries, = Number of entries in page table x Page table entry size. If the memory is byte-addressable, then size of one location = 1 byte. Which one of the following is the maximum number of bits that can be used for storing protection and other information in each page table entry? The hit ratio is clearly related to the number of associative registers. Let ‘n’ number of bits are required. Watch video lectures by visiting our YouTube channel LearnVidFun. 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) Number of locations possible with 22 bits = 2, It is given that the size of one location = 2 bytes, Number of bits in virtual address = 32 bits. Page Table: stores where in memory each page is, Main Memory : divided into page frames, a space large enough to hold one page of data If the memory is word-addressable where 1 word = m bytes, then size of one location = m bytes. Physical Address: The physical address is an address in a computer that is represented in binary numbers. is power of 2, e.g., 4k = 2^12, to determine the page number, shift the address right by 12 bits, if the virtual address size = 32 bits, then since the page size is 4k = 2^12, Use the following considerations for page file sizing for all versions of Windows and Windows Server. In a virtual memory system, size of virtual address is 32-bit, size of physical address is 30-bit, page size is 4 Kbyte and size of each page table entry is 32-bit. A deeper MMU descriptor level means more kernel memory for page tables. address in the process, A = 10,000, page number = 10000 / 4k = 10,000 / 4096 = 2.xxx = truncate to 2, this calculation is done quickly on the computer since the page size the first 32- 12 = 20 bits give the page number, this is the distance from the beginning of the page, page offset = 10000 mod 4k = 10,000 mod 4096 = 1908, to determine the page offset, mask out all but the rightmost 12 bits, look up the page number in the page table and obtain the frame number, to create the physical address, frame = 17 bits; offset = 12 bits; then, a translation lookaside buffer (TLB) is used, associative cache, where cache is the fastest memory available and (heap, stack, static, variables), 3. take a page from a ready process that has not been referenced for a long time, 4. take a page that has not been modified since it was swapped in, 5. take a page that has been referenced recently by a ready process, assume the complete process is first loaded into the swap space, more pages go back and forth between swap space and main memory, when a program is loaded, put it into the swap space, memory and page size is always a power of 2, this is the page number within the process address space, e.g. method (based on FIFO) and a global page replacement method ( e.g. Paging is a non-contiguous memory allocation technique. Important Formulas of Paging. How to calculate Physical Address: Logical Address = Segment : Offset … The 16-bit segment, 16-bit offset. the processor and the ready list, status To gain better understanding about solving numerical problems on paging, Next Article- Optimal Page Size | Practice Problems. A deeper MMU descriptor level means more time spent in page table traversal. ratio of 80 to 98 percent can be obtained. Consider a machine with 64 MB physical memory and a 32 bit virtual address space. is now ``waiting for main memory'', fetch " page in " => bring a page into main memory, fetch a page when it is referenced but not stored in main memory, causes a page fault whenever a new page is required, disadvantage - cold start fault: many page faults when a process is just starting, advantage - no unnecessary pages are ever fetched, guess which pages will be required soon and fetch them before they are referenced, make sure to fetch all pages in a process' working set before restarting, intent is that all pages required soon are in main memory when the process starts, when a page is fetched, also fetch the next page(s) in the process address space, common variant is to fetch pairs of pages whenever one is referenced, the extra page may be before or after - used in Windows NT, WIndows 2000, programmer/compiler adds hints to the OS about what pages will be needed soon, problem: cannot trust programmers; they will hint that all their pages are important, determine where to put the page that has been fetched, easy for paging, just use any free page frame, determines which page should be removed from main memory (when a page must be fetched), want to find the least useful page in main memory, danger: do not want to swap out pages from a process that is trying to bring pages into main memory, where the system is preoccupied with moving pages in and out of memory, feature: the disk can be very busy while the CPU is nearly idle, one cure is to reduce the number of processes in main memory, Example: Windows NT/XP/Vista use both a local page replacement Consider a system with byte-addressable memory, 32 bit logical addresses, 4 kilobyte page size and page table entries of 4 bytes each.

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