GATE | GATE CS 2013 | Question 65

In a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The lines in set s are sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards. The main memory block numbered j must be mapped to any one of the cache lines from.
(A) (j mod v) * k to (j mod v) * k + (k-1)
(B) (j mod v) to (j mod v) + (k-1)
(C) (j mod k) to (j mod k) + (v-1)
(D) (j mod k) * v to (j mod k) * v + (v-1)


Answer: (A)

Explanation: Number of sets in cache = v. So, main memory block j will be mapped to set (j mod v), which will be any one of the cache lines from (j mod v) * k to (j mod v) * k + (k-1).
(Associativity plays no role in mapping- k-way associativity means there are k spaces for a block and hence reduces the chances of replacement.)


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