Q54

Consider a $32$-bit system with $4 \mathrm{~KB}$ page size and page table entries of size $4$ bytes each. Assume $1 \mathrm{~KB}=2^{10}$ bytes. The OS uses a $2$-level page table for memory management, with the page table containing an outer page directory and an inner page table. The $\text{OS}$ allocates a page for the outer page directory upon process creation. The $\text{OS}$ uses demand paging when allocating memory for the inner page table, i.e., a page of the inner page table is allocated only if it contains at least one valid page table entry. An active process in this system accesses $2000$ unique pages during its execution, and none of the pages are swapped out to disk. After it completes the page accesses, let $\text{X}$ denote the minimum and $\text{Y}$ denote the maximum number of pages across the two levels of the page table of the process. The value of $\text{X+Y}$ is ___________.