For the following questions, consider a paged memory system that has a physical main memory size of 1MB (2²⁰) and a page frame size (and hence page size) of 32KB (2¹⁵). Consider a process P whose logical address space is 512KB (2¹⁹).

Important Note: If an answer requires an exponent, use the ^ character. For example: 2¹⁵ would be entered as 2^15.

1. How many physical page frames are there in the above paged memory system? Your answer should be in exponential form.

2. How many bits are needed to represent a physical page frame number in the system?

3. How many logical pages are there for P? Your answer should be in exponential form.

4. How many bits are needed to represent a logical page number for P?