Consider a nontrivial cache memory organization with m > 1 lines in which the…
2017
Consider a nontrivial cache memory organization with m > 1 lines in which the cache is divided into v sets, each of which consists of k lines. The set-associative mapping reduces to direct mapping when:
Answer: C. v = m and k = 1 — CONCEPT — A v-set, k-way set-associative cache contains m = v × k cache lines. Direct mapping is the one-way special case: every set contains exactly one…
- A.
v = m and k = m
- B.
v = 1 and k = m
- C.
v = m and k = 1
- D.
v = 1 and k = 1
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Correct answer: C
CONCEPT — A v-set, k-way set-associative cache contains m = v × k cache lines. Direct mapping is the one-way special case: every set contains exactly one candidate cache line, so k = 1.
APPLICATION — For the stated nontrivial cache, substituting k = 1 into m = v × k gives m = v × 1 = v. Therefore the matching pair is v = m and k = 1.
CONTRAST — The remaining pairs describe different organizations or capacities:
v = m and k = m gives v × k = m² lines, not the stated m lines when m > 1.
v = 1 and k = m gives one set holding all m lines, the fully associative case.
v = 1 and k = 1 gives a one-line cache, which conflicts with the stated m > 1 capacity.
CROSS-CHECK — With v = m and k = 1, each block index selects exactly one of m sets, and that set contains exactly one line. This reproduces the defining placement rule of a direct-mapped cache.