CDA3101 Test 3 Review Problem Set Solutions
1. Assume a 2-way set-associative cache with 16 cache sets, 1 word per block, and an LRU
replacement policy. For both a write-through, no write-allocate and a write-back, write-allocate
cache, fill in the appropriate information for the following memory references
16 cache sets  24 cache sets  4 index bits
1 word/block  4 bytes/block  22 bytes/block  2 offset bits
92
28
94
24
88
216
26
0101 1100
0001 1100
0101 1110
0001 1000
0101 1000
1101 1000
0001 1010
Write Through / No Write Allocate
Type
Address
Tag
Index
Offset
Result
Memref
R
R
W
W
R
W
R
92
28
94
24
88
216
26
1
0
1
0
1
3
0
7
7
7
6
6
6
6
0
0
2
0
0
0
2
Miss
Miss
Hit
Miss
Miss
Miss
Miss
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Update
Cache?
Yes
Yes
Yes
No
Yes
No
Yes
Write Back / Write Allocate
Type
Address
Tag
Index
Offset
Result
Memref
R
R
W
W
R
W
R
92
28
94
24
88
216
26
1
0
1
0
1
3
0
7
7
7
6
6
6
6
0
0
2
0
0
0
2
Miss
Miss
Hit
Miss
Miss
Miss
Miss
Yes
Yes
No
Yes
Yes
Yes (2)
Yes
Update
Cache?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
2. Consider a virtual memory scheme with a 4KB page size. We have a direct-mapped TLB with 4
entries. A virtual address is 20 bits and a physical address is 18 bits. How many virtual pages are
allowed? How many physical pages are allowed? How many bits are used for the page offset, TLB
index, and TLB tag?
- Virtual pages: 256 pages
- Physical pages: 64 pages
- Page offset: 12 bits
- TLB index: 2 bits
- TLB tag: 6 bits
3. The following table is a stream of virtual addresses as seen on a system. Assume 1KB pages, an
initially empty 2-way set associative TLB with 4 sets and true LRU replacement. If pages must be
brought in from disk, assign the next available physical page number.
9452
6388
10944
5540
6200
1244
5548
0010 0100 1110 1100
0001 1000 1111 0100
0010 1010 1100 0000
0001 0101 1010 0100
0001 1000 0011 1000
0000 0100 1101 1100
0001 0101 1010 1100
Page Table
Index
0
1
2
3
4
5
6
7
8
9
10
11
Valid
1
1
0
1
1
1
01
1
0
01
1
0
Physical Page Number or Disk
2
6
Disk
5
4
3
Disk 8
1
Disk
Disk 7
0
Disk
Given the two address streams in the table above, for each stream show the final state of the system
given the initial state of the TLB and Page Table. Also, for each reference, indicate whether it was a hit
in the TLB, a hit in the page table, or a page fault. What is the physical address that corresponds to
every virtual address?
Virtual
Address
9452
6388
10944
5540
6200
1244
5548
Virtual
Page #
9
6
10
5
6
1
5
Page
Offset
236
244
704
420
56
220
428
TLB
Tag
2
1
2
1
1
0
1
TLB
Index
1
2
2
1
2
1
1
TLB
Result
Miss
Miss
Miss
Miss
Hit
Miss
Hit
Page Table
Result
Miss
Miss
Hit
Hit
Hit
-
Physical
Page #
7
8
0
3
8
6
3