Operating Systems #Page-table-size

Question

Main-Memory Size=64MB, Logical address-32bits long, Page size-4KB,

What is the total space wasted in maintaining the page table?

  Solⁿ- 2²⁰(No. of pages) * 2B(14bits~2B)(frame-address-bits) = 2MB

In this question why we consider the total no of pages in the secondary memory as the number of  entries in the page table? 

The Main Memory can hold only that much pages as much frames it has.

So, shouldn't we consider the no. of frames in main memory as the no. of page table entries?

I don't know why such confusions come in such a crucial time! Please answer and clear my confusion asap!

Answer 1

Page table size =  Total no of page table entries * single entry size ( no of bits required to represent main memory).

                       = 2^20 * 26 bits
Note:- Each page table contains information about all page entries of a process present in the virtual memory.

Comments

If the page is not present in the MM, still do we need to map? We can store the frame no. and page no in the page table right? which would require only that much entries which we can accomodate in MM.

@Shubham Shukla 6 pls help me understand it in a better way.

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@Ashish Goyal 3
its not like page will always be present in main memory when needed page will be brought into main memory so accordingly mapping would be done from page table,so page table is kind of information repository.
And the thing you are saying that only pages present in main memory should be stored in page table that's not correct.
And Yes frame number would only be stored for those pages only which are present in main memory, for rest it would be null.
So TLB concept you must be knowing, TLB is referred first, than page table present if there is a hit in page table for corresponding page which we are looking for than we don't need to refer memory to bring that page in, so if we don't keep information abt all pages here than would it be possible tell me.?
You must get your doubt cleared now.!

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Thanks @Shubham Shukla 6 for the elaboration.

Regarding your question-

 if there is a hit in page table for corresponding page which we are looking for than we don't need to refer memory to bring that page in, so if we don't keep information abt all pages here than would it be possible tell me.? 

I would say YES! It would be possible. You see, it totally depends on what data structure we choose for storing the page table. If we store the page no and corresponding frame no.'s of the pages in main memory, we would easily be able to find out whether the referred page is in the M/m or not. If present, we can get the frame no. too. It just requires a hash table.

But I think your such beautiful elaborate explanation has cleared my doubt. Although hash table decreases the search time near to const. but still it would add up the some search time which would be huge overhead as compared with the CPU cycle time, and as we know time is more precious than memory, so we go with storing entries for all the  pages in the page table. 

Thanks a lot.:-) ;-)