: Assume that a system consists of 64 KB of physical address space (RAM). The op

Question

: Assume that a system consists of 64 KB of physical address space (RAM). The operating system allows each process to use a logical address space of size 1MB. The frame size is 256 bytes.

How many bits are used for the logical address generated by the CPU while executing the programs?

How many frames are there in this system?

How many bits of the logical address are used for identifying page number? How many bits are used as offset within a page?

How many entries are there in each page table? Assuming each entry requires 4 bytes, what is the size of page table for each process?

Given the page table below, what physical address will be generated by the paging unit for each of the logical address?

Page Table

Page Number

Frame Number

Valid/Invalid bit

0

0x0F

v

1

0x02

v

2

0x13

v

3

-

i

4

-

i

5

-

i

6

-

i

7

-

i

Logical Address

Physical Address (in binary)

0x00012

0x00541

0x00254

0x00190

0x01050

NOTE: one hex digit = 4 bits (one hex digit can have values from 0 to F)

Page Table

Page Number

Frame Number

Valid/Invalid bit

0

0x0F

v

1

0x02

v

2

0x13

v

3

-

i

4

-

i

5

-

i

6

-

i

7

-

i

Explanation / Answer

How many bits are used for the logical address generated by the CPU while executing the programs?
Answer: Since its of size 1MB => 220 => 20 bits for logical address

How many frames are there in this system?
Answer: Since physical memory is of size 64KB => 26 *210 => 216   for physica address
and frame size is 28 => Number of Page frames = 216 / 28 = 256

How many bits of the logical address are used for identifying page number? How many bits are used as offset within a page?

Answer: Since logical dddress is 20 bits => 20 - 8 = 12 bits for identifying page number
and 8 bits  bits are used as offset within a page

How many entries are there in each page table? Assuming each entry requires 4 bytes, what is the size of page table for each process?

Answer: Number of enteries = 256 , if Size is 4 bytes.
Size of page table is : 1KB

Given the page table below, what physical address will be generated by the paging unit for each of the logical address?

1) 0x00012 : first 12 bits 0x000 is mapped to 0x0F and last 8 bits will be foffset
Physical address will be 0x0F12
2) 0x00541 : first 12 bits 0x005 is Invalid
3) 0x00254 : first 12 bits 0x002 is mapped to 0x13 and last 8 bits will be offset
Physical address will be 0x1354
4)0x00190 : first 12 bits 0x001 is mapped to 0x02 and last 8 bits will be offset
Physical address will be 0x0290
5) 0x01050 : first 12 bits 0x010 is Invalid

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