Question

Suppose that a main memory has 8192 blocks each block having 32 words. Show the memory address format (see figures 4.10 and 4.12 of your textbook for examples) for each of the cache organizations below.

a. a direct map cache with 64 lines of 32 words each

b. a set associative cache with 16 sets each with four lines of 32 words each

c. a fully associate cache with 128 lines of 32 words each

PLEASE EXPLAIN IN DETAIL

Answer 1

Number of blocks in Main memory size = 8192= 2¹³

Block Size = 32 Words = 2⁵ words

Memory Size = 2¹³ * 2⁵ = 2¹⁸ words

Memory address = 18 bits

a) Direct Map Cache

Number of lines = 64 = 2⁶ => Line offset = 6 bits

Line Size = 32 Words = 2⁵ => Word offset = 5 bits

Remaining Tag bits = 18 - 5 - 6 = 7 bits

Tag	Line Offset	Word Offset
7	6	5

b) 4-Way Set-associative Cache

Number of Sets = 16 = 2⁴ => Set offset = 4 bits

Line Size = 32 Words = 2⁵ => Word offset = 5 bits

Remaining Tag bits = 18 - 5 - 4 = 9 bits

Tag	SetOffset	Word Offset
9	4	5

c) Fully-associative Cache

Number of Lines = 128 = 2⁷

Line Size = 32 Words = 2⁵ => Word offset = 5 bits

Remaining Tag bits = 18 - 5 = 13 bits

Fully associative cache only have tag and word offset as it directly maps main memory block.

Tag	Word Offset
13	5