Problem 4. Consider a cache memory that can hold 64K lines of data. The micropro

Question

Problem 4. Consider a cache memory that can hold 64K lines of data. The microprocessor using this cache has 40 address lines. Fill in the table below Organization-Line Size: 16 bytes One-Way Set | Tag width = Associative Index Width- LineSize 32Bytes ? Line Size: 64 Bytes Tag width = Index Width Offset Width Line Size: 128 Bytes Tag Width Index Width rag Width = Index Width- Offset Width = WidthOffset Width Two-Way Set Associative Tag Width | Index Width = Tag Width = Index Width- Offset Width ag width = Index Width- Offset Width 1 Tag width Index Width = Offset Width Tag Width Index width = Offset Width- Tag Width Index Width Offset width = Tag Width Index Width- Offiset Width Offset Width Four-Way Set Tag Width- Associative | Index Width Tag Width- Index Width- Tag Width- Index width Offset WidthOffset Width Tag Width- Index width = Offset Width = Tag Width- Index Width Offset Width Offset Width- Eight-Way Set Tag Width- Associative | Index Width offset width = Tag Width Offset Width Tag Width Index width = Offset Width Tag Width Index Width Offset Width Fully Associative Index Width

Explanation / Answer

firstly,i'll give the general formula for calculating tag width,index width and offset width.

offset width = log2(line size)

index width = log2(cache size / p-way)

tag width = (number of address lines) - (index width).

Also,in fully assciative there is no index width.

Tag width = 40 - 16 = 24

index width =log2(64K/1)= 16

offset width= 4

Tag width = 40 - 16 = 24

index width = log2(64K/1)= 16

offset width= 5

Tag width = 40 - 16 = 24

index width =

log2(64K/1)= 16

offset width= 6

Tag width =40 - 16 = 24

index width =log2(64K/1)= 16

offset width= 7

Tag width = 40 - 15 = 25

index width = log2(64K/2) = 15

offset width= 4

Tag width = 25

index width =log2(64K/2) = 15

offset width= 5

Tag width = 25

index width =15

offset width= 6

Tag width = 25

index width =15

offset width= 7

Tag width = 40 - 14 = 26

index width = log2(64K/4) = 14

offset width= 4

Tag width = 26

index width = 14

offset width= 5

Tag width = 26

index width = 14

offset width= 6

Tag width = 26

index width = 14

offset width= 7

Tag width = 40 - 13 = 27

index width = log2(64K/8) = 13

offset width= 4

Tag width = 27

index width = 13

offset width= 5

Tag width =27

index width = 13

offset width= 6

Tag width =27

index width = 13

offset width= 7

Tag width =40

index width =0

offset width= 4

Tag width =40

index width =0

offset width= 5

Tag width =40

index width =0

offset width= 6

Tag width =40

index width =0

offset width= 7

Organisation Line size: 16 bytes Line size: 32 bytes Line size: 64 bytes Line size: 128 bytes one-way set associative

Tag width = 40 - 16 = 24

index width =log2(64K/1)= 16

offset width= 4

Tag width = 40 - 16 = 24

index width = log2(64K/1)= 16

offset width= 5

Tag width = 40 - 16 = 24

index width =

log2(64K/1)= 16

offset width= 6

Tag width =40 - 16 = 24

index width =log2(64K/1)= 16

offset width= 7

two-way set associative

Tag width = 40 - 15 = 25

index width = log2(64K/2) = 15

offset width= 4

Tag width = 25

index width =log2(64K/2) = 15

offset width= 5

Tag width = 25

index width =15

offset width= 6

Tag width = 25

index width =15

offset width= 7

four-way set associative

Tag width = 40 - 14 = 26

index width = log2(64K/4) = 14

offset width= 4

Tag width = 26

index width = 14

offset width= 5

Tag width = 26

index width = 14

offset width= 6

Tag width = 26

index width = 14

offset width= 7

eight-way set associative

Tag width = 40 - 13 = 27

index width = log2(64K/8) = 13

offset width= 4

Tag width = 27

index width = 13

offset width= 5

Tag width =27

index width = 13

offset width= 6

Tag width =27

index width = 13

offset width= 7

fully associative

Tag width =40

index width =0

offset width= 4

Tag width =40

index width =0

offset width= 5

Tag width =40

index width =0

offset width= 6

Tag width =40

index width =0

offset width= 7

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