Project ForgeComputer Organization & Architecture
Memory Hierarchy & Floating Point
GATE 2013
Hard
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
- (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)
Explanation
Block j maps to set number (j mod v). Since the k lines of set s occupy the sequential line range s·k to s·k+(k−1), substituting s=(j mod v) gives the cache line range (j mod v)·k to (j mod v)·k + (k−1).
Source: GATE CS 2013 (2013)
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