Question

A hypothetical computer has 16 MB RAM and has a word size of 32 bits. It has cache memory having 32 blocks having a block size of 64 bits. Show how the main memory address 100110001111101110111100 will be mapped to a cache address, if (i) Direct cache mapping is used (ii) Associative cache mapping is used (iii) Two way set associative cache mapping is used.

Answer 1

Given:

Main memory Size = 64 Words

Main Memory word size = 16 bits

Cache Memory Size = 8 Blocks

Cache Memory Block size = 32 bits

⇒1 Block of Cache = 2 Words of RAM

⇒Memory location address 25 is equivalent to Block address 12.

⇒ Total number of possible Blocks in Main Memory = 64/2 = 32 blocks.



Associative Mapping:

The block can be anywhere in the cache.

Direct Mapping:

Size of Cache = 8 blocks

Location of Block 12 in Cache = 12 modulo 8 = 4

2 Way set associative mapping:

Number of blocks in a set = 2

Number of sets = Size of Cache in blocks / Number of blocks in a set

= 8 / 2 = 4

Block 12 will be located anywhere in (12 modulo 4) set, that is set 0.