Consider a computer system with 4 GB memory and 1MB cache with 256-byte block (l

Question

Consider a computer system with 4 GB memory and 1MB cache with 256-byte block (line) size. a) Find the size in bits of byte offset, line/set index, and tag in case of direct mapping, full-associative, 2-way set associative, and 4-way set associative. b) For the memory reference of address 0 times 87651234. Show the values (in Hexadecimal) of the byte offset, line/set index, and tag in each of the four cases above. c) Considering 2-way set associative mapping, complete the table below and explain the actions taken for the memory access sequence of operations given in the first column:

Explanation / Answer

Given that Main memory = 4GB = 229 bytes.

Therefor physical address = 29 bytes.
  
cache memory = 1MB = 220

Block size = 256 bytes = 28

Therefore byte offset = 8

Therefore no.of lines = cachesize/blocksize
= 220 / 28
=212.
no. of lines = 12.

Direct mapping:
.............

In direct mapping , no. of lines = Index

Therefore index= 12

Then Tag = PHYSICAL ADDRESS-INDEX-BYTEOFF
= 32-12-8
= 12 bytes.

Tag

Index

Byteoff

12

12

8

2-way set associiative:
.........................

In 2-way set associative ,index = line size/2
= 212/2
= 211

Therefore index= 11

Then Tag = PHYSICAL ADDRESS-INDEX-BYTEOFF
= 32-11-8
= 13 bytes.

Tag

Index

Byteoff

13

11

8

4-way set associiative:
.........................

In 4-way set associative ,index = line size/4
= 212 / 22
= 210

Therefore index= 10

Then Tag = PHYSICAL ADDRESS-INDEX-BYTEOFF
= 32-10-8
= 14 bytes.

Tag

Index

Byteoff

14

10

8

Tag

Index

Byteoff

12

12

8

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