Question

Q1. Suppose we have a virtual memory of size 2 Terabytes (2048GB, or 2⁴¹ bytes), where pages are 8KB (2¹³ bytes) each, and the machine has 4GB (2³² bytes) of physical memory.

                     a) Compute the number of page table entries needed if all the pages are being used.

                      b) Compute the size of the page table if each page table entry also required 4 additional bits (valid, protection, dirty, use).

Q2. For this problem, you are given a system with a virtual memory. The virtual memry hads the following configuration –

                 -Physical addresses are 8 bits long, but only 27 = 128 bytes of physical memory is installed, at physical addresses 0 up to 127.

                 -Pages are 24 = 16 bytes long. Virtual addresses are 10 bits long.

                 -An exception will be raised if a program accesses a virtual address whose virtual page has no mapping in the page table. Exception will also be raise if this is mapped to a physical page outside of installed physical memory.

                 -The main memory contents are shown in Table 1. To find the physical address of a byte, you need to read the least significant digit from the column label and the most significant digit from the row label. For example, the shaded byte in the second row is at physical address 0x12. All entries are in hexadecimal.

                                                  Table 1: Main Memory

	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
0x0	4e	65	76	65	72	20	67	6f	6e	6e	61	20	67	69	76	65
0x1	20	79	6f	75	20	75	70	0a	4e	65	76	65	72	20	67	6f
0x2	6e	6e	61	20	6c	65	74	20	79	6f	75	20	64	6f	77	6e
0x3	0a	4e	65	76	65	72	20	67	6f	6e	6e	61	20	72	75	6e
0x4	20	61	72	6f	75	6e	64	20	61	6e	64	20	64	65	73	65
0x5	72	74	20	79	6f	75	0a	4e	65	76	65	72	20	67	6f	6e
0x6	6e	61	20	6d	61	6b	65	20	79	6f	75	20	63	72	79	0a
0x7	4e	65	76	65	72	20	67	6f	6e	6e	61	20	73	61	79	20

The page table is shown in Table 2. The virtual page number in the left column is mapped to the
physical page number in the second column. Virtual page numbers are listed in binary.

                                                  Table 2: Page Table

Virtual page	Physical page
0	0x2
1	0x4
10	0x1
11	0x5
100	0x4
101	0x7
110	0x9

a) List the four bytes in the word beginning at physical address 0x34.
b) How many virtual addresses refer to the first byte of the shaded word in row 0x2 ? List them
ALL.
c) How many virtual addresses refer to the first byte of the shaded word in row 0x4 ? List them
ALL.

d) List all virtual addresses that refer to the first byte of the shaded word in row 0x6.

e) If the program loads a word from virtual address 0x5C (01011100), write down what data is
returned?
f) What is the result if the program loads a word from virtual address 0x64 (01100100)?

Answer 1

o) given 41 Logical Addres Stoci, LAS 2 bles which ts Space, LAs2 41 LA = Fnreal) Address stace, PAS = 232 h tes which goes 32 ranne o PA ame mo 13 m bitz bits page table enties (re)-21-ト- (41-13) 2 No.叶 28 b size of PTE,e bde required to rebresent a fame taddhonal bis [m-ト) +4: 32-1344 = 19 +4 = 23 2 5