Consider a logical address space of $8$ pages; each page is $2048$ byte long, mapped onto a physical memory of $64$ frames. Solve the following questions:

a$.$ What are the sizes of the logical and physical spaces?

b$.$ How many bits are there in the logical address and how many bits are there in the physical address?

c$.$ A process of size $6284$ bytes will be loaded in some of the available frames$=\{10,8,40,25,3,15,56,18,12,35\}.$ Write how many pages needed for this process and then display the contents of the process$$s page table.

d$.$ What is the size of the internal fragment?

e$.$ Convert the following logical addresses $2249$ and $10512$ to physical addresses.