Project ForgeComputer Organization & Architecture
Memory Hierarchy & Floating Point
GATE 2008
Expert
(Same 64KB, 2-way set associative, 16-byte-block cache and 1024×1024 double array ARR stored in row-major order, starting at a virtual page boundary.) Which of the following array elements has the same cache index as ARR[0][0]?
- AARR[0][4]
- ARR[4][0]
- CARR[0][5]
- DARR[5][0]
Explanation
ARR[i][j] byte offset = (i×1024+j)×8. ARR[0][0] offset=0, set index=(0/16) mod 2048=0. We need another offset that's a multiple of 16×2048=32768 bytes. ARR[4][0] offset = 4×1024×8 = 32768 bytes exactly — set index = 32768/16 mod 2048 = 2048 mod 2048 = 0, matching. The other options give set indices 2, 2, and 512 respectively.
Source: GATE CS 2008 (2008)
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