Operating Systems | Memory Management | Question 10

Consider data given in the above question. What is the minimum number of page colours needed to guarantee that no two synonyms map to different sets in the processor cache of this computer? (GATE CS 2013)
(A) 2
(B) 4
(C) 8
(D) 16


Answer: (C)

Explanation:

1 MB 16-way set associative virtually indexed physically tagged cache(VIPT). 
The cache block size is 64 bytes.

No of blocks is 2^20/2^6 = 2^14.

No of sets is 2^14/2^4 = 2^10.

VA(46)
+-------------------------------+
tag(30) , Set(10) , block offset(6)
+-------------------------------+

In VIPT if the no. of bits of page offset = 
                  (Set+block offset) then only one page color is sufficient.

but we need 8 colors because the number bits where the cache set index and 
physical page number over lap is 3 so 2^3 page colors is required.(option 
c is ans). 

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