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As we know segmented paging is an improvement over segmentation and paging but I am having some doubts regarding the memory overhead of these three system.It is clear that segmentation need less memory overhead.But about other two system please confirm these two points.

number of pages in pure paging=number of pages in segmented paging

In pure paging we have a single page table for each process but in segmentation we have page table for each segment.so I think that after all total number of pages in pure paging is equal to Segmented paging.is this true?

memory overhead is larger in segmented paging than pure paging

as the number of pages are same,thus total memory requirements will be same but in paging we have a fixed size single page table so some amount of internal fragmention will be there but as in segmented paging there are various size of many segmented page table so can I conclude that amount of frag mention is much more than pure paging and also extra segmentation table is required in this system.
Is my conclusion is true that memory overhead is more in segmented page table?

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It is difficult to compare directly because memory management will likely be different in segmented paging compared to pure paging. That being said, if we assume the allocations are exactly the same, then segmented has a higher overhead because one needs to keel track of the segments. However the overhead will depend on the number of segments, and there are several possible strategies and it is also hardware dependent. Some processor may support an arbitrary (or at least very high) number of segments whereas some may only support a few (data/code/stack for example).

Also note that segmented paging is not used in any of the major processors these days: ARM does not support it, x86 only supports it in 32-bit and almost no OS uses it.

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