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The size of the physical address space of a processor is 2P bytes. The word length is 2W bytes. The capacity of cache memory is 2N bytes. The size of each cache block is 2M words. For a K-way set-associative cache memory, the length (in number of bits) of the tag field is
- a)P − N − log2K
- b)P − N + log2K
- c)P − N − M − W − log2K
- d)P − N − M − W + log2K
Correct answer is option 'B'. Can you explain this answer?
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The size of the physical address space of a processor is 2Pbytes. The ...
Physical Address Space = 2P Bytes. Word Length is 2W bytes, which means each word is of size 2W bytes. Cache memory size = 2N Bytes and Tag Size = 2X Bytes. Physical address is P - W bits Number of blocks in cache = 2(N-W-M) It is a K-way set associative cache memory, each set in cache will have K-blocks. So, Number of sets = 2(N-W-M)/ K SET bits will be N-W-M-logk Offset bits will be M We know, TAG bits = Main memory bits - SET bits - offset bits So, TAG bits(x) = P - W - (N-M-W-logk)- M = P - W - N + M + W + logk - M x = P - N + logk Option (B) is Correct.
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The size of the physical address space of a processor is 2Pbytes. The ...
Understanding Cache Memory and Tag Field Calculation
To determine the length of the tag field in a K-way set-associative cache, we need to analyze the components of the memory architecture.
Key Parameters:
- Physical Address Space: 2^P bytes
- Word Length: 2^W bytes
- Cache Memory Capacity: 2^N bytes
- Cache Block Size: 2^M words
Calculating Cache Parameters:
1. Total Cache Lines:
- Cache size in bytes divided by block size in bytes gives the number of cache lines.
- Cache size = 2^N bytes
- Block size = 2^M words * 2^W bytes/word = 2^(M + W) bytes
- Total lines = 2^N / 2^(M + W) = 2^(N - M - W)
2. Number of Sets:
- For a K-way set-associative cache, the number of sets is total lines divided by K.
- Number of sets = (2^(N - M - W)) / K = 2^(N - M - W - log2(K))
3. Address Breakdown:
- The physical address consists of the tag, index, and block offset.
- The block offset is determined by the block size: log2(block size) = M + W.
- The index consists of the number of sets: log2(number of sets) = N - M - W - log2(K).
Tag Field Calculation:
- The tag field length can be derived from the physical address size:
- Tag length = P (total address bits) - Index length - Block offset length
- Tag length = P - (N - M - W - log2(K)) - (M + W)
- Simplifying gives us: Tag length = P - N + log2(K).
Conclusion:
- The correct answer for the length of the tag field in the K-way set-associative cache is:
P - N + log2(K)
Thus, the correct option is B.
To determine the length of the tag field in a K-way set-associative cache, we need to analyze the components of the memory architecture.
Key Parameters:
- Physical Address Space: 2^P bytes
- Word Length: 2^W bytes
- Cache Memory Capacity: 2^N bytes
- Cache Block Size: 2^M words
Calculating Cache Parameters:
1. Total Cache Lines:
- Cache size in bytes divided by block size in bytes gives the number of cache lines.
- Cache size = 2^N bytes
- Block size = 2^M words * 2^W bytes/word = 2^(M + W) bytes
- Total lines = 2^N / 2^(M + W) = 2^(N - M - W)
2. Number of Sets:
- For a K-way set-associative cache, the number of sets is total lines divided by K.
- Number of sets = (2^(N - M - W)) / K = 2^(N - M - W - log2(K))
3. Address Breakdown:
- The physical address consists of the tag, index, and block offset.
- The block offset is determined by the block size: log2(block size) = M + W.
- The index consists of the number of sets: log2(number of sets) = N - M - W - log2(K).
Tag Field Calculation:
- The tag field length can be derived from the physical address size:
- Tag length = P (total address bits) - Index length - Block offset length
- Tag length = P - (N - M - W - log2(K)) - (M + W)
- Simplifying gives us: Tag length = P - N + log2(K).
Conclusion:
- The correct answer for the length of the tag field in the K-way set-associative cache is:
P - N + log2(K)
Thus, the correct option is B.
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The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer?
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The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer?.
The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The size of the physical address space of a processor is 2Pbytes. The word length is 2Wbytes. The capacity of cache memory is 2Nbytes. The size of each cache block is 2Mwords. For a K-way set-associative cache memory, the length (in number of bits) of the tag field isa)P − N − log2Kb)P − N + log2Kc)P − N − M − W − log2Kd)P − N − M − W + log2KCorrect answer is option 'B'. Can you explain this answer?.
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