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If the associativity of a processor cache is doubled while keeping the capacity and block size unchanged, which one of thefollowing is guaranteed to be NOT affected?
- a)Width of tag comparator
- b)Width of set index decoder
- c)Width of way selection multiplexer
- d)Width of processor to main memory data bus
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the associativity of a processor cache is doubled while keeping the...
If associativity is doubled, keeping the capacity and block size constant, then the number of sets gets halved. So, width of set index decoder can surely decrease - (B) is false.
Width of way-selection multiplexer must be increased as we have to double the ways to choose from- (C) is false
As the number of sets gets decreased, the number of possible cache block entries that a set maps to gets increased. So,
we need more tag bits to identify the correct entry. So, (A) is also false.
(D) is the correct answer- main memory data bus has nothing to do with cache associativity- this can be answered without
even looking at other options.
Width of way-selection multiplexer must be increased as we have to double the ways to choose from- (C) is false
As the number of sets gets decreased, the number of possible cache block entries that a set maps to gets increased. So,
we need more tag bits to identify the correct entry. So, (A) is also false.
(D) is the correct answer- main memory data bus has nothing to do with cache associativity- this can be answered without
even looking at other options.
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Most Upvoted Answer
If the associativity of a processor cache is doubled while keeping the...
Explanation:
When the associativity of a processor cache is doubled while keeping the capacity and block size unchanged, it means that the number of sets in the cache is halved. In other words, each set in the cache will now contain twice the number of cache lines compared to before.
Let's consider the impact of this change on the different components of the cache:
1. Width of tag comparator:
The tag comparator is responsible for comparing the tag bits of the memory address being accessed with the tag bits stored in the cache. The width of the tag comparator depends on the number of bits in the tag field. When the associativity is doubled, the number of sets is halved, but the block size remains the same. Therefore, the number of bits required for the tag field does not change. Hence, the width of the tag comparator remains unaffected.
2. Width of set index decoder:
The set index decoder is responsible for decoding the set index bits of the memory address being accessed. The width of the set index decoder depends on the number of sets in the cache. When the associativity is doubled, the number of sets is halved. Therefore, the number of bits required for the set index field is reduced. Hence, the width of the set index decoder will be halved.
3. Width of way selection multiplexer:
The way selection multiplexer is responsible for selecting the cache line from the set based on the set index bits. The width of the way selection multiplexer depends on the number of cache lines per set. When the associativity is doubled, the number of sets is halved, but the block size remains the same. Therefore, the number of cache lines per set remains unchanged. Hence, the width of the way selection multiplexer remains unaffected.
4. Width of processor to main memory data bus:
The width of the processor to main memory data bus is unrelated to the cache associativity. It is determined by the design of the processor and the memory system. Changing the associativity of the cache does not impact the width of the data bus.
Therefore, the width of the processor to main memory data bus is guaranteed to be not affected when the associativity of a processor cache is doubled while keeping the capacity and block size unchanged.
When the associativity of a processor cache is doubled while keeping the capacity and block size unchanged, it means that the number of sets in the cache is halved. In other words, each set in the cache will now contain twice the number of cache lines compared to before.
Let's consider the impact of this change on the different components of the cache:
1. Width of tag comparator:
The tag comparator is responsible for comparing the tag bits of the memory address being accessed with the tag bits stored in the cache. The width of the tag comparator depends on the number of bits in the tag field. When the associativity is doubled, the number of sets is halved, but the block size remains the same. Therefore, the number of bits required for the tag field does not change. Hence, the width of the tag comparator remains unaffected.
2. Width of set index decoder:
The set index decoder is responsible for decoding the set index bits of the memory address being accessed. The width of the set index decoder depends on the number of sets in the cache. When the associativity is doubled, the number of sets is halved. Therefore, the number of bits required for the set index field is reduced. Hence, the width of the set index decoder will be halved.
3. Width of way selection multiplexer:
The way selection multiplexer is responsible for selecting the cache line from the set based on the set index bits. The width of the way selection multiplexer depends on the number of cache lines per set. When the associativity is doubled, the number of sets is halved, but the block size remains the same. Therefore, the number of cache lines per set remains unchanged. Hence, the width of the way selection multiplexer remains unaffected.
4. Width of processor to main memory data bus:
The width of the processor to main memory data bus is unrelated to the cache associativity. It is determined by the design of the processor and the memory system. Changing the associativity of the cache does not impact the width of the data bus.
Therefore, the width of the processor to main memory data bus is guaranteed to be not affected when the associativity of a processor cache is doubled while keeping the capacity and block size unchanged.
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If the associativity of a processor cache is doubled while keeping the capacity and block size unchanged, which one of thefollowing is guaranteed to be NOT affected?a)Width of tag comparatorb)Width of set index decoderc)Width of way selection multiplexerd)Width of processor to main memory data busCorrect answer is option 'D'. Can you explain this answer?
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