Paging Examples

1
Paging Examples

• Assume a page size of 1K and a 15-bit logical
  address space.
• How many pages are in the system?

2
Paging Examples

• Assume a page size of 1K and a 15-bit logical
  address space.
• How many pages are in the system?
• How many bits are required to address each
  byte within a 1024-byte page?

3
Paging Examples

• Assume a page size of 1K and a 15-bit logical
  address space.
• How many pages are in the system?
• How many bits are required to address each
  byte within a 1024-byte page? 10 (210 1024).
• This leaves 5 bits for page number.
• So, How many pages are in the system?

4
Paging Examples

• Assume a page size of 1K and a 15-bit logical
  address space.
• How many pages are in the system?
• How many bits are required to address each
  byte within a 1024-byte page? 10 (210 1024).
• This leaves 5 bits for page number.
• So, How many pages are in the system?
• 32 (25 32)

5

• Now consider a 15-bit address space with 8
  logical pages. How large are the pages?

6

• Assuming a 15-bit address space with 8 logical
  pages. How large are the pages?
• Answer 212 4K. It takes 3 bits to reference 8
  logical pages (23 8). This leaves 12 bits for
  the page size and thus pages are 212.

7
Consider logical address 2049 and the following
page table for some process P0. Assume a 15-bit
address space with a page size of 1K. What is
the physical address to which logical address
2049 will be mapped?
8
0 3
8
Consider logical address 2049 and the following
page table for some process P0. Assume a 15-bit
address space with a page size of 1K. What is
the physical address to which logical address
2049 will be mapped?
Logical Pages
Step 1. Convert logical address to
binary Logical address 000100000000001
0 1 2 3 4
8
0 3
9
Logical Pages
Step2. Determine the logical page number Since
there are 5-bits allocated to the logical page,
the address is broken up as follows 00010
0000000001 Logical page number offset within
page
0 1 2 3 4
10
00010
00011
Step 3. Use logical page number as an index into
the page table to get physical page number.
Logical Address 00010 0000000001
11
00010
000110000000001
Step 4. Concatenate offset with physical page
frame number Logical Address 00010 0000000001
12
0 1 2 3 4
0
1024
2048
3072 P0.2
4096
000110000000001 3073