Suppose that the OS has setup the following page tables for process 1:
and for process 2:
entry index entry address page address present
----------- ------------------ ------------ -------
0 CR3_1 + 0 * 4 0x00001 1
1 CR3_1 + 1 * 4 0x00000 1
2 CR3_1 + 2 * 4 0x00003 1
3 CR3_1 + 3 * 4 0
...
2^20-1 CR3_1 + 2^20-1 * 4 0x00005 1
entry index entry address page address present
----------- ----------------- ------------ -------
0 CR3_2 + 0 * 4 0x0000A 1
1 CR3_2 + 1 * 4 0x12345 1
2 CR3_2 + 2 * 4 0
3 CR3_2 + 3 * 4 0x00003 1
...
2^20-1 CR3_2 + 2^20-1 * 4 0xFFFFF 1
Before process 1 starts running, the OS sets its
cr3
to point to the page table 1 at CR3_1
.When process 1 tries to access a linear address, this is the physical addresses that will be actually accessed:
linear physical
--------- ---------
00000 001 00001 001
00000 002 00001 002
00000 003 00001 003
00000 FFF 00001 FFF
00001 000 00000 000
00001 001 00000 001
00001 FFF 00000 FFF
00002 000 00003 000
FFFFF 000 00005 000
To switch to process 2, the OS simply sets
cr3
to CR3_2
, and now the following translations would happen:
linear physical
--------- ---------
00000 002 0000A 002
00000 003 0000A 003
00000 FFF 0000A FFF
00001 000 12345 000
00001 001 12345 001
00001 FFF 12345 FFF
00004 000 00003 000
FFFFF 000 FFFFF 000
Step-by-step translation for process 1 of logical address
0x00000001
to physical address 0x00001001
:- split the linear address into two parts:
| page (20 bits) | offset (12 bits) |
So in this case we would have: *page = 0x00000. This part must be translated to a physical location. *offset = 0x001. This part is added directly to the page address, and is not translated: it contains the position _within_ the page. - look into Page table 1 because
cr3
points to it. - The hardware knows that this entry is located at RAM address
CR3 + 0x00000 * 4 = CR3
: *0x00000
because the page part of the logical address is0x00000
*4
because that is the fixed size in bytes of every page table entry - since it is present, the access is valid
- by the page table, the location of page number
0x00000
is at0x00001 * 4K = 0x00001000
. - to find the final physical address we just need to add the offset:
00001 000 + 00000 001 --------- 00001 001
because00001
is the physical address of the page looked up on the table and001
is the offset.We shift00001
by 12 bits because the pages are always aligned to 4KiB.The offset is always simply added the physical address of the page. - the hardware then gets the memory at that physical location and puts it in a register.
Another example: for logical address
0x00001001
:- the page part is
00001
, and the offset part is001
- the hardware knows that its page table entry is located at RAM address:
CR3 + 1 * 4
(1
because of the page part), and that is where it will look for it - it finds the page address
0x00000
there - so the final address is
0x00000 * 4k + 0x001 = 0x00000001
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