(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.