In virtual memory systems, addresses are divided into two parts: A virtual page number $($VPN$)$ used to look up the physical page location and a page offset that tells us the specific byte location within a page. When translating addresses, remember that while the physical page location may change, the position within a page $($the offset$)$ remains the same. After all, we're looking for the same byte position, just on a different page!

Consider a system with the following specifications:

$-32-$bit virtual address space

$-$ Page size of $4096$ bytes

$-$ Single$-$level page table

$-$ Given virtual address: $0$x$99$AABBCC

$-$ Page table entry for this address contains: $0$x$00$B$77000$

Answer the following to transkate the virtual address to its physical address:

$1.$ How many bits are needed to represent different positions within a $4096-$byte page? $($the offset$)$

$2.$ How many bits remain for the virtual page number?

$3.$ Break down your given virtual address $($Hint: translate it to binary and then back to hex for easier understanding$)$

$1.$ What portion represents the VPN$?$

$2.$ Which portion represents the offset?

$4.$ Use your given page table entry. This gives you the base address of where this page is stored in physical memory, think about what part of your original address needs to be changed and what part stays the same.

$5.$ Construct the final physical address. Consider using the information from the page table and parts of your original address.

Show all your work, including:

$-$ Your bit calculations

$-$ The binary$/$hex breakdown of addresses