CS $3101$ Computer Organization

Homework $6($Please answer with the correct answers$)$

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Suppose a computer using direct mapped cache has $2^{32}$ words of main memory, and a

cache of $1024$ blocks, where each cache block contains $32$ words.

a$.$ How many blocks of main memory are there?

b$.$ What is the format of a memory address as seen by the cache, i$.$e$,$ what are the

sizes of the tag, block, and offset fields?

c$.$ To which cache block will the memory reference $0003101A_{16}$ map?

Suppose a computer using fully associative cache has $2^{24}$ words of main memory and a

cache of $512$ blocks, where each cache block contains $16$ words.

a$.$ How many blocks of main memory are there?

b$.$ What is the format of a memory address as seen by the cache, i$.$e$.,$ what are the

sizes of the tag and offset fields?

c$.$ To which cache block will the memory reference $17042416$ map?

$($bonus question, $5$ points$)$ Suppose a computer using set associative cache has $2^{16}$ words

of main memory and a cache of $128$ blocks, and each cache block contains $8$ words.

a$.$ If this cache is $2-$way set associative, what is the format of a memory address as

seen by the cache, that is$,$ what are the sizes of the tag, set, and offset fields?

b$.$ If this cache is $4-$way set associative, what is the format of a memory address as

seen by the cache?