Why do we need hashed page tables for Paging in Operating Systems?
There are several advantages of hashed page tables over the standard flat/hierarchal page tables. One of these being size, a hashed page table will use less space in memory than using a flat or hierarchal page table. It will at most have one entry for every physical frame (worst case scenario; unlikely  as many page numbers will end up having same hash value) instead of having an entry for every page (many of which will be left unused; although this problem is alleviated with the use of hierarchal page tables). Inverted page tables also have this advantage, however hashed page tables have a performance advantage over inverted tables, as the lookup is much faster in hashed page table. So a hashed page table combines the space advantage of an inverted table with the lookup advantage of a standard page table.