Question

Consider a computer with a 256 byte address space and a two way 64 byte set associative cache. The computer word size is a byte and each cache line contains four bytes. If the cache is initially empty and the following sequence of hexadecimal addresses is read, show the cache contents and the the corresponding sequence of hits and misses. 48, 0C, 48, 4C, 5C, 3A, 20, 21, 22, 24, 81, 49, 30, 34, 27, 3E, 24, 28, 2C, 40

Answer 1

Memory Size = 256 Bytes => Address = 8 bits

Cache Size = 64 Bytes

Line/Block Size = 4 Bytes => Byte offset = 2 bits

Number of blocks in set = 2

Number of Sets in Cache = 64/(4*2) = 8 => set index = 3

Tag bits = 8-2-3 = 3 bits

Address

Hit/Miss

Set 0

Set 1

Set 2

Set 3

Set 4

Set 5

Set 6

Set 7

Block 0

Block 1

Block 0

Block 1

Block 0

Block 1

Block 0

Block 1

Block 0

Block 1

Block 0

Block 1

Block 0

Block 1

Block 0

Block 1

48 = 010 010 00

Miss

48 - 51

0C = 000 011 00

Miss

48 - 51

0C - 0F

48 = 010 010 00

Hit

48 - 51

4C = 010 011 00

Miss

48 - 51

0C - 0F

4C - 4F

5C = 010 111 00

Miss

48 - 51

0C - 0F

4C - 4F

5C - 5F

3A = 001 110 10

Miss

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

20 = 001 000 00

Miss

20 - 23

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

21 = 001 000 01

Hit

20 - 23

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

22 = 001 000 10

Hit

20 - 23

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

24 = 001 001 00

Miss

20 - 23

24 - 27

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

81 = 100 000 01

Miss

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

49 = 010 010 01

Hit

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

38 - 3B

5C - 5F

30 = 001 100 00

Miss

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

30 -33

38 - 3B

5C - 5F

34 = 001 101 00

Miss

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

30 -33

34 - 37

38 - 3B

5C - 5F

27 = 001 001 11

Hit

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

30 -33

34 - 37

38 - 3B

5C - 5F

3E = 001 111 10

Miss

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

30 - 33

34 - 37

38 - 3B

5C - 5F

3C - 3F

24 = 001 001 00

Hit

20 - 23

80 - 83

24 - 27

48 - 51

0C - 0F

4C - 4F

30 - 33

34 - 37

38 - 3B

5C - 5F

3C - 3F

28 = 001 010 00

Miss

20 - 23

80 - 83

24 - 27

48 - 51

28 - 31

0C - 0F

4C - 4F

30 - 33

34 - 37

38 - 3B

5C - 5F

3C - 3F

2C = 001 011 00

Miss

20 - 23

80 - 83

24 - 27

48 - 51

28 - 31

2C - 2F

4C - 4F

30 - 33

34 - 37

38 - 3B

5C - 5F

3C - 3F

40 = 010 000 00

Miss

40 - 43

80 - 83

24 - 27

48 - 51

28 - 31

2C - 2F

4C - 4F

30 - 33

34 - 37

38 - 3B

5C - 5F

3C - 3F