GATE 2013 CS (CS1) – Question 63
Virtual addresses are 46 bits, physical addresses 32 bits. A three-level page table has one-page T₁, entries of T₁ pointing to T₂ pages and T₂ entries pointing to T₃ pages. T₃ entries are 32-bit PTEs. The processor has a 1 MB, sixteen-way, virtually indexed physically tagged cache with 64-byte blocks. What is the minimum page-colour count to keep synonyms in the same cache set?
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Correct answer: (C) 8
Explanation
Page size from the table organization is 8 KiB. Cache capacity per way is 1 MiB/16=64 KiB, so virtual set selection extends beyond the page offset by log₂(64/8)=3 bits. Controlling those bits requires 2³=8 colours, C. Equivalently colours=cache capacity/(associativity×page size).