Caches

Question $1$:

An n$-$way set$-$associative cache consists of several sets, each of which consists of n blocks. Each block in the memory maps to a unique set in the cache given by the index field, and a block can be placed in any element of that set. Figure below shows an example of a direct mapped, $2-$way set associative, $4-$way set associative, and fully associative cache with $8$ blocks.

$\backslash$table$[[0,],[1,],[2,],[3,],[4,],[5,],[6,],[7,]]$

Data

$\backslash$table$[[0,$Block $0],[$Block $1],[1,$Block $0],[$Block $1],[3,$Block $0],[$Block $1],[4,$Block $0],[$Block $1]]$

Data

$\backslash$table$[[0,$Block $0],[1,$Block $1],[$Block $2],[$Block $3],[$Block $0],[,$Block $1],[,$Block $2],[,$Block $3]]$

Set #

$\backslash$table$[[$Block $0],[$Block $1],[$Block $2],[$Block $3],[$Block $4],[$Block $5],[$Block $6],[$Block $7]]$

Data

Direct Mapped Cache

Two$-$way set associative

Four$-$way set associative

Fully associative

Consider a memory system that uses $32-$bit memory addresses and a cache with a block size of $64$ bytes.

a$.$ Assume a direct mapped cache with a tag field in the address of $18$ bits. Determine the number of cache blocks, and the number of bits required for the byte offset.

b$.$ Assume a fully associative cache. Determine the number of bits required for the byte offset.

c$.$ Assume a four$-$way set$-$associative cache with a tag field size of $10$ bits. Determine the number of cache sets, the number of cache blocks, and the number of bits required for the byte offset.