Consider a system with paging-based memory management, whose architecture allows for a 4GB virtual address space for processes. The size of logical pages and physical frames is 4KB. The system has 8GB of physical RAM. The system allows a maximum of 1K processes to run concurrently and uses a 10-bit number to represent the PID. (Assume 1K = 1024.) 

A)  Assuming the OS uses hierarchical paging; calculate the maximum memory space required to store the page tables of all processes in the system. Assume that each page table entry requires an additional 10 bits (beyond the frame number) to store various flags. Assume page table entries are rounded up to the nearest byte. Consider the memory required for both outer and inner page tables in your calculations. 

B)  Now assume the OS uses an inverted page table instead of hierarchical page tables. Every inverted page table entry needs to store the process identifier along with the page number. Assume that inverted page table entries are rounded up to the nearest byte. Calculate the memory required to store the inverted pag e table in the system.