Question

1. The following page table is for a system with 16-bit virtual and physical addresses and with 4,096-byte pages. The reference bit is set to 1 when the page has been referenced. Periodically, a thread zeroes out all values of the reference bit. A dash for a page frame indicates the page is not in memory. The page-replacement algorithm is localized LRU, and all numbers are provided in decimal.

Page	Page Frame	Reference Bit
0	7	0
1	6	0
2	15	0
3	13	0
4	14	0
5	8	0
6	−	0
7	0	0
8	4	0
9	9	0
10	1	0
11	−	0
12	2	0
13	3	0
14	−	0
15	5	0

Convert the following virtual addresses (in hexadecimal) to the equivalent physical addresses. You may provide answers in either hexadecimal or decimal. (10 points)

Show the calculation steps (10 points)

Also set the reference bit for the appropriate entry in the page table. (10 points)

• 0xB55C

• 0x9A9D

• 0x6EE8

Answer 1

Page Size = 4096 Bytes => Byte Offset = 12 bits

#Page Index = 16 - 12 = 4 bits

0xB55C

=> Page Index = 0xB = 11₁₀

=> Byte Offset = 0x55C

=> At page index 11 in page table, page frame is not available so physical address can't be found.

=> Invalid address

0x9A9D

=> Page Index = 0x9 = 9₁₀

=> Byte Offset = 0xA9D

=> At page index 9 in page table, page frame = 9

=> Physical Address = 0x9A9D

0x6EE8

=> Page Index = 0x6 = 6₁₀

=> Byte Offset = 0xEE8

=> At page index 6 in page table, page frame is not available so physical address can't be found.

=> Invalid address

After referencing above virtual addresses

Page	Page Frame	Reference Bit
0	7	0
1	6	0
2	15	0
3	13	0
4	14	0
5	8	0
6	−	1
7	0	0
8	4	0
9	9	1
10	1	0
11	−	1
12	2	0
13	3	0
14	−	0
15	5	0