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.

Listed below are some operating system abstractions (in the left column) and the hardware components. Which matching pairs is correct?

$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$List-$${\rm I}$$
(a) Thread $$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$(b) Virtual Address space
(c) File System $$\,\,\,\,\,\,\,\,\,\,$$(d) Signal

$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$List-$${\rm II}$$
(1) Interrupt $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$(2) Memory
(3) $$CPU$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$(4) Disk

A multi-user, multi-processing operating system cannot be implemented on hardware that does not support:

System calls are usually invoked by using: