Q48

Consider a three-level page table to translate a $39-$bit virtual address to a physical address as shown below:

The page size is $\text{4 KB} \;(1\text{KB}=2^{10}$ bytes$)$ and page table entry size at every level is $8$ bytes. A process $P$ is currently using $2\text{GB}\;(1 \text{GB}=2^{30}$ bytes$)$ virtual memory which is mapped to $2\text{GB}$ of physical memory. The minimum amount of memory required for the page table of $P$ across all levels is _________ $\text{KB}$.