A computer system uses $$32$$-bit virtual address, and $$32$$-bit physical address. The physical memory is byte addressable, and the page size is $$4$$ kbytes. It is decided to use two level page tables to translate from virtual address to physical address. Equal number of bits should be used for indexing first level and second level page table, and the size of each page table entry is $$4$$ bytes.

(a) Give a diagram showing how a virtual address would be translated to a physical address.

(b) What is the number of page table entries that can be contained in each page?

(c) How many bits are available for storing protection and other information in each page table entry?

A certain computer system has the segmented paging architecture for virtual memory. The memory is byte addressable. Both virtual and physical address spaces contain $${2^{16}}$$ bytes each. The virtual address space is divided into $$8$$ non-overlapping equal size segments. The memory management unit $$(MMU)$$ has a hardware segment table, each entry of which contains the physical address of the page table for the segment. Page table are stored in the main memory and consists of $$2$$ byte page table entries.

(a)$$\,\,\,\,\,$$ What is the minimum page size in bytes so that the page table for a segment requires at most one page to store it? Assume that the page size can only be a power of $$2.$$

(b)$$\,\,\,\,\,$$ Now suppose that the pages size is $$512$$ bytes. It is proposed to provide a $$TLB$$ (Translation look-aside buffer) for speeding up address translation. The proposed $$TLB$$ will be capable of storing page table entries for $$16$$ recently referenced virtual pages, in a fast cache that will use the direct mapping scheme. What is the number of tag bits that will need to be associated with each cache entry

(c)$$\,\,\,\,\,$$ Assume that each page table entry contains (besides other information) $$1$$ valid bit, $$3$$ bits for page protection and $$1$$ dirty bit. How many bits are available in page table entry for storing the aging information for the page? Assume that the page size is $$512$$ bytes.

In a computer system where the ‘best-fit’ algorithm is used for allocating ‘jobs’ to ‘memory partitions’, the following situation was encountered:

When will the $$20$$ $$K$$ job complete?

A demand paged virtual memory system uses $$16$$ bit virtual address, page size of $$256$$ bytes, and has $$1$$ Kbyte of main memory. $$LRU$$ page replacement is implemented using a list, whose current status (page numbers in decimal ) is
$$\eqalign{ & \,\, \uparrow \cr & LRU\,Page \cr} $$
For each hexa decimal address in the address sequence given below,
$$00FF,$$ $$010D,$$ $$10FF,$$ $$11B0$$
Indicate,
i) The new status of the list
ii) Page faults, if any, and
iii) Page replacements, if any