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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?
- a)2
- b)4
- c)8
- d)16
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider data given in theabove question. What is the minimum number o...
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.
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)
+-------------------------------+
+-------------------------------+
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).
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).
Most Upvoted Answer
Consider data given in theabove question. What is the minimum number o...
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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Community Answer
Consider data given in theabove question. What is the minimum number o...
To guarantee that no two synonyms map to different sets in the processor cache of the computer, we need to ensure that each synonym is assigned a unique set in the cache. This can be achieved by using a technique called cache coloring, where each set in the cache is assigned a unique color. The number of colors needed corresponds to the minimum number of page colors required.
Here's how we can determine the minimum number of page colors needed:
1. Determine the cache size: The cache size is given as 8 KB, which means it can hold 8 * 1024 bytes of data.
2. Determine the cache line size: The cache line size is given as 32 bytes.
3. Calculate the number of cache lines: Divide the cache size by the cache line size to get the number of cache lines. In this case, 8 * 1024 / 32 = 256 cache lines.
4. Determine the number of cache sets: The number of cache sets is determined by the cache associativity. In this case, the associativity is 4, so the number of sets is 256 / 4 = 64.
5. Determine the number of synonyms: The number of synonyms is given as 512.
6. Calculate the minimum number of page colors: Divide the number of synonyms by the number of cache sets to get the minimum number of page colors. In this case, 512 / 64 = 8.
Therefore, the minimum number of page colors needed to guarantee that no two synonyms map to different sets in the processor cache of this computer is 8.
Here's how we can determine the minimum number of page colors needed:
1. Determine the cache size: The cache size is given as 8 KB, which means it can hold 8 * 1024 bytes of data.
2. Determine the cache line size: The cache line size is given as 32 bytes.
3. Calculate the number of cache lines: Divide the cache size by the cache line size to get the number of cache lines. In this case, 8 * 1024 / 32 = 256 cache lines.
4. Determine the number of cache sets: The number of cache sets is determined by the cache associativity. In this case, the associativity is 4, so the number of sets is 256 / 4 = 64.
5. Determine the number of synonyms: The number of synonyms is given as 512.
6. Calculate the minimum number of page colors: Divide the number of synonyms by the number of cache sets to get the minimum number of page colors. In this case, 512 / 64 = 8.
Therefore, the minimum number of page colors needed to guarantee that no two synonyms map to different sets in the processor cache of this computer is 8.
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