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A computer system has a main memory consisting of $1$M $16$-bit words. It also has a $4$K-word cache organized in the block-set-associative manner (with $4$ blocks per set and $64$ words per block).

Assume that the cache is initially empty. The processor fetches $4352$ words from locations $0, 1, 2,  \dots, 4351$, in that order. It then repeats this fetch sequence nine more times. If the cache is $10$ times faster than the main memory, estimate the $improvement factor$ resulting from the use of the cache. [Assume that the LRU algorithm is used for block replacement.]

  1. $3.19$
  2. $3.16$
  3. $2.15$
  4. $2.19$
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