How to calculate which virtual logical address corresponds to physical address?

Question

Assume that the page table for the process currently running on the processor looks as shown in the figure below. All numbers are decimal, all numbers starting with 0 and all addresses are memory syllable addresses. The page size is 1024 bytes.

Which physical address (if any) does each of the following logical (virtual) addresses correspond to? Indicates if a page error occurs while translating the title.

Which physical address (if any) does each of the following logical (virtual) addresses correspond to? Indicates if a page error occurs while translating the title. a) 1085 b) 2321 c) 5409

number of pages	valid/invalid bit	number of frames
0	1	4
1	1	7
2	0	-
3	1	2
4	0	-
5	1	0

I don't want the solution for this problem, I want someone to explain how this kind of problems are solved.

Answer 1

I think you can guess most configuration from the question. I'll take a) as an example. Maybe you can tell me if I get the answer right and then you can solve the rest by yourself?

The first step is to determine what is the part of the virtual address representing the offset in the page table, and the part representing the offset in the physical frame. For address 1085 and page size of 1024 bytes, you need 10 bits for the offset in the physical frame and the rest for the offset in the page table.

1085 decimal = 0x43D = 0b100 0011 1101

The ten least significant bits (to the right) are the offset in the physical frame. That is 0b00 0011 1101 = 0x3D = 61 decimal. So now you know that the offset in the physical frame will be 61 bytes.

To calculate in what page this offset will be, you take the leftover bits (to the left). That is 0b1 = 0x1 = 1 decimal. This references page table entry 1. Page table entry 1 has the valid bit set. It means that the page is present in memory and will not cause a page fault. The page table entry points to frame number 7. There are 7 frames before frame 7: frames 0, 1, 2, 3, 4, 5, and 6. Thus this virtual address should translate to 7 * 1024 + 61 = 7229.