Paging Examples

Assume a page size of 1K and a 15-bit logical address space.

How many pages are in the system?

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?

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 (2^10 = 1024).

This leaves 5 bits for page number.

So, How many pages are in the system?

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 (2^10 = 1024).

This leaves 5 bits for page number. So, How many pages are in the system?

32 (2^5 = 32)

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

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

• Answer: 2^12 = 4K. It takes 3 bits to reference 8 logical pages (2^3 = 8). This leaves 12 bits for the page size and thus pages are 2^12.

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

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

Step 1. Convert logical address to binary:

Logical address:

000100000000001

0

1

2

3

4

Logical Pages

8

0

3

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

Logical Pages

Step 3. Use logical page number as an index into the page table to get physical page number.

Logical Address:

00010 0000000001

00010

8

0

3 00011

Step 4. Concatenate offset with physical page frame number

Logical Address

00010 0000000001

00010

8

0

3 000110000000001

8

0

3

P0.1

2048

1024

0

3072 P0.2

4096

000110000000001 = 3073

0

1

2

3

4