Caches are important to providing a high-performance memory hierarchy to processors. Below is a list of...

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Caches are important to providing a high-performance memory hierarchy to processors. Below is a list of memory address refere

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Answer 1

Answer #1

Given,

Size of block = 2 words

Number of bits in cache offset = log ( block size ) = log 2 = 1 bit

Cache size = 8 words

Number of lines = Cache size / block size = 8 / 2 = 4

Number of bits in the index = log 4 = 2 bits

Let the address be expressed in terms of 8 bits

Then,

tag bits = Address bits - ( Offset bits + Index bits ) = 8 - ( 1 + 2 ) = 5 bits

1.

The first address in decimal is 1.

The binary address is 00000001.

Tag = 00000

Index = 00

Offset = 1

It is a miss as this address is accessed for the first time.

The cache is :

Index	Tag	Memory Address mapped
00	00000	M[1]
01
10
11

2.

The next address is 4.

The binary address is 00000100.

Tag = 00000

Index = 10

Offset = 0.

It is a miss as this address is accessed for the first time.

Index	Tag	Memory Address mapped
00	00000	M[1]
01
10	00000	M[4]
11

3.

The next address is 8.

The binary address is 00001000.

Tag = 00001

Index = 00

Offset = 0.

This is a conflict miss as the tag does not match with the tag at index 0.

Index	Tag	Memory Address mapped
00	00001	M[8]
01
10	00000	M[4]
11

4.

The next address is 5.

The binary address is 00000101.

Tag = 00000

Index = 10

Offset = 1.

This is a hit as the tag matches with the tag in index 10.

Index	Tag	Memory Address mapped
00	00001	M[8]
01
10	00000	M[5]
11

5.

The next address is 20.

The binary address is 00010100.

Tag = 00010

Index = 10

Offset = 0.

This is a miss as the tag does not match with the tag in index 10.

Index	Tag	Memory Address mapped
00	00001	M[8]
01
10	00010	M[20]
11

6.

The next address is 17.

The binary address is 00010001.

Tag = 00010

Index = 00

Offset = 1.

This is a conflict miss.

Index	Tag	Memory Address mapped
00	00010	M[17]
01
10	00010	M[20]
11

7.

The next address is 4.

The binary address is 00000100.

Tag = 00000

Index = 10

Offset = 0.

This is a miss as the tag does not match with the tag in index 10.

Index	Tag	Memory Address mapped
00	00010	M[17]
01
10	00000	M[4]
11

8.

The next address is 56.

The binary address is 00111000.

Tag = 00111

Index = 00

Offset = 0.

This is a miss as the tag does not match with the tag in index 00.

Index	Tag	Memory Address mapped
00	00111	M[56]
01
10	00000	M[4]
11

9.

The next address is 9.

The binary address is 00001001.

Tag = 00001

Index = 00

Offset = 1.

This is a miss as the tag does not match with the tag in index 00.

Index	Tag	Memory Address mapped
00	00001	M[9]
01
10	00000	M[4]
11

10.

The next address is 10.

The binary address is 00001010.

Tag = 00001

Index = 01

Offset = 0.

This is compulsory miss.

Index	Tag	Memory Address mapped
00	00001	M[9]
01	00001	M[10]
10	00000	M[4]
11

11.

The next address is 43.

The binary address is 00101011.

Tag = 00101

Index = 01

Offset = 1.

This is a miss as the tag does not match with the tag in index 01.

Index	Tag	Memory Address mapped
00	00001	M[9]
01	00101	M[43]
10	00000	M[4]
11

12.

The next address is 5.

The binary address is 00000101.

Tag = 00000

Index = 10

Offset = 1.

This is a hit as the tag matches with the tag in index 10.

Index	Tag	Memory Address mapped
00	00001	M[9]
01	00101	M[43]
10	00000	M[5]
11

13.

The next address is 6.

The binary address is 00000110.

Tag = 00000

Index = 11

Offset = 0.

This is a compulsory miss.

Index	Tag	Memory Address mapped
00	00001	M[9]
01	00101	M[43]
10	00000	M[5]
11	00000	M[6]

14.

The next address is 9.

The binary address is 00001001.

Tag = 00001

Index = 00

Offset = 1.

This is a hit as the tag matches with the tag in index 00.

Index	Tag	Memory Address mapped
00	00001	M[9]
01	00101	M[43]
10	00000	M[5]
11	00000	M[6]

15.

The next address is 17.

The binary address is 00010001.

Tag = 00010

Index = 00

Offset = 1.

This is a miss as the tag does not match with the tag in index 00.

Index	Tag	Memory Address mapped
00	00010	M[17]
01	00101	M[43]
10	00000	M[5]
11	00000	M[6]

Hence, the final table is :

Decimal address	Binary address	Tag	Index	Offset	Miss or Hit
1	00000001	00000	00	1	Miss
4	00000100	00000	10	0	Miss
8	00001000	00001	00	0	Miss
5	00000101	00000	10	1	Hit
20	00010100	00010	10	0	Miss
17	00010001	00010	00	1	Miss
4	00000100	00000	10	0	Miss
56	00111000	00111	00	0	Miss
9	00001001	00001	00	1	Miss
10	00001010	00001	01	0	Miss
43	00101011	00101	01	1	Miss
5	00000101	00000	10	1	Hit
6	00000110	00000	11	0	Miss
9	00001001	00001	00	1	Hit
17	00010001	00010	00	1	Miss

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