Memory Management

A system has a Translation Lookaside Buffer (TLB) that has a reach of 1 MB. TLB reach is defined as the total amount of physical memory that can be accessed through the TLB entries. The paging system uses pages of size 4 KB. The virtual address space is 64 GB and physical address space is 1 GB. If each TLB entry stores a 4-bit process id, page number, frame number, and a 2-bit control field, then the size of the TLB (in bytes) is ___________. (*answer in integer*) Note: 1K $= 2^{10}$, 1M $= 2^{20}$, 1G $= 2^{30}$

Consider contiguous allocation of physical memory to processes using variable partitioning scheme. Suppose there are 8 holes in the memory of sizes 20 KB, 4 KB, 25 KB, 18 KB, 7 KB, 9 KB, 15 KB, and 12 KB. Assume that no two holes are adjacent. Two processes P1 of size 16 KB and P2 of size 9 KB arrive in that order, and they are allocated memory using the best-fit technique. After allocating space to P1 and P2, the number of holes of size less than 8 KB is ____________. (*answer in integer*) Note: 1K $= 2^{10}$

A computer system supports a logical address space of $2^{32}$ bytes. It uses two-level hierarchical paging with a page size of 4096 bytes. A logical address is divided into a $b$-bit index to the outer page table, an offset within the page of the inner page table, and an offset within the desired page. Each entry of the inner page table uses eight bytes. All the pages in the system have the same size. The value of $b$ is ___________. (Answer in integer)

Which of the following tasks is/are the responsibility/responsibilities of the memory management unit (MMU) in a system with paging-based memory management?

Consider a 32-bit system with 4 KB page size and page table entries of size 4 bytes each. Assume 1 KB = $2^{10}$ bytes. The OS uses a 2-level page table for memory management, with the page table containing an outer page directory and an inner page table. The OS allocates a page for the outer page directory upon process creation. The OS uses demand paging when allocating memory for the inner page table, i.e., a page of the inner page table is allocated only if it contains at least one valid page table entry. An active process in this system accesses 2000 unique pages during its execution, and none of the pages are swapped out to disk. After it completes the page accesses, let $X$ denote the minimum and $Y$ denote the maximum number of pages across the two levels of the page table of the process. The value of $X + Y$ is __________

Consider a three-level page table to translate a 39-bit virtual address to a physical address as shown below.

<-------------- 39-bit virtual address -------------->
 ----------------------------------------------------
| Level 1  | Level 2  | Level 3  |    Page    |
| offset   | offset   | offset   |   offset   |
|__________|__________|__________|____________|
  9 bits     9 bits     9 bits      12 bits

The page size is 4KB (1KB $= 2^{10}$ bytes) and page table entry size at every level is 8 bytes. A process $P$ is currently using 2GB (1GB $= 2^{30}$ bytes) virtual memory which is mapped to 2GB of physical memory. The minimum amount of memory required for the page table of $P$ across all levels is ________ KB.

Consider six memory partitions of sizes 200 KB, 400 KB, 600 KB, 500 KB, 300 KB and 250 KB, where KB refers to kilobyte. These partitions need to be allotted to four processes of sizes 357 KB, 210 KB, 468 KB and 491 KB in that order. If the best fit algorithm is used, which partitions are NOT allotted to any process?