1. Dec 13, 2010

### naspek

1. The problem statement, all variables and given/known data

A virtual memory system has a page size of 512 bytes, seven virtual pages, and four
physical page frames. The page table is as follows:
VPN.........PFN
0..............2
1..............0
2..............-
3..............1
4..............3
5..............-
6..............-
Note: VPN -> Virtual Page Number, PFN -> Page Frame Number

What physical address, if any, would each of the following virtual addresses
correspond to?
i. 0
ii. 2010
iii. 2046
iv. 3030
v. 1026

3. The attempt at a solution

i. 0============ 0000 0000 0000
ii. 2010========= 0111 1101 1010
iii. 2046========= 0111 1111 1110
iv. 3030======== 1011 1101 0110
v. 1026======== 0100 0000 0010

i've translate it to binary number already..
but.. i don't how to proceed..
can someone plz guide me..

2. Dec 13, 2010

### Staff: Mentor

I don't think converting the virtual address to binary is much help. I'm not certain, but I think what you need to do is to find the virtual page number for each virtual address, and then see which physical page that VPN is mapped to.

To do this, divide the virtual address by 512 using integer division. For example, your second virtual address is 2010. 2010/512 == 3, so the virtual page number is 3. From the information you provided, virtual page 3 maps to physical page 1.

3. Dec 13, 2010

### naspek

thanks for the idea..

now.. i proceed...

ii. 2010===== 2010/512
==========3.93 = 3 , virtual page number 3 maps to physical page 1..
but.. how do i get the physical address then?

4. Dec 13, 2010

### Staff: Mentor

The remainder (or modulus) gives you the offset in the memory page. In C notation, this is 2010 % 512 == 474. In mathematical notation, this is 2010 (mod 512) = 474.

5. Dec 13, 2010

### naspek

get it.. then i need to change 474 to binary number to get my physical address?

6. Dec 13, 2010

### Staff: Mentor

I don't see why you would need to do that. It's just an address. It could be 474 (decimal) or 1DA (hex) or 111011010 (binary). These all represent the same number, but in different bases.

7. Dec 13, 2010

### naspek

thanks for the clarification.. but..
why do i need the table if, i can just do the calculation(divide by 512 and get the answer already)..?

8. Dec 13, 2010

### Staff: Mentor

There's an important part you're missing. Rather than me telling you what it is, I will let you figure it out.

9. Dec 13, 2010

### naspek

the physical address is 0001 1101 1010.. right?

10. Dec 13, 2010

### Staff: Mentor

How did you get that?

11. Dec 13, 2010

### naspek

2010 mod 512 = 474

i change 474 into 12 bits binary number.. so.. i get 0001 1101 1010.. right?

12. Dec 13, 2010

### Staff: Mentor

The 474 is just the offset within the page, but which page are we talking about? And by that, I mean, which physical page?

13. Dec 13, 2010

### naspek

ok... so..

VPN.........PFN
3..............1

it's on physical page 1.. right?

is it 1 is my physical address? can't be.. too odd...

14. Dec 13, 2010

### Staff: Mentor

Yes, physical page 1. That's where the table comes in, so that you can translate a virtual page number to a physical page number.

OK, you have physical page 1, and an offset of 447. What's the physical address?

15. Dec 13, 2010

### naspek

ok... physical page number constitutes the upper portion of the physical address, while the page offset, constitutes the lower portion

1 | 0001 1101 1010

correct?

16. Dec 13, 2010

### Staff: Mentor

No, that's too big. It would be helpful if you didn't change the numbers into binary. Your physical address is calculated using this formula:
physical address = (physical page number) * 512 + offset

17. Dec 13, 2010

### naspek

ok.. thanks for the formula..

*got question here.. is it [(physical page number)*512] + offset or..
................................. (physical page number) * (512 + offset)
the first one or the second formula is correct?

physical address = (1) * 512 + 474
.......................= 986 @ 0011 1101 1010
now.. this is the correct one?

18. Dec 13, 2010

### Staff: Mentor

It's this one: (physical page number)*512 + offset

And 986 is the correct address.

To check: 986 / 512 = 1
and 986 (mod 512) = 474

19. Dec 13, 2010

### naspek

geez!! thanks mark44!
but.. if i'm going to answer it in binary number format..
how should i know the number of bits of the physical address?

20. Dec 13, 2010

### Staff: Mentor

The offset is 0 - 511, or 0 - 0x1ff, or 1 1111 1111, so that takes 9 bits.

The physical page number is a multiple of 512 (0, 1, 2, or 3 times 512), so the largest physical address will be 3*512 + 511 = 2047 = 0x7ff, which fits in 11 bits.