Analyze the virtual memory system below and solve for the requested information:

$-$ Virtual Address Space: $4$ GB

$-$ Page Size: $4$ KB

$-$ Physical Memory: $512$ MB

i$.$ How many bits are used for the virtual page number $($VPN$)$ and page offset in the virtual address?

ii$.$ How many bits are required for the physical frame number $($PFN$)$ in the physical address? How many pages are in the virtual address space, and how many frames are in the physical memory?

iii. Draw the block diagram to show all the components with their sizes.