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A 4-way set-associative cache has lines of 32 byte and a total cache size of 16 KB. Which of the following main memory block is mapped onto the set '13' of the cache memory when 16 MB of main memory is used?
- a)A295DO
- b)FCED9D
- c)2FAODO
- d)FOA1B5
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A 4-way set-associative cache has lines of 32 byte and a total cache s...
As we know,
Number of lines = 16/32 = 214/25
Number of lines = 16/32 = 214/25
= 29
Number of sets = 29/22 = 27
Cache representation:
Physical address size = 16 MB = 24 bit
⇒ 24 = x + 7 + 5
⇒ x = 12 bit
Now, to map physical memory at 13th set bit (b11 b10 b9 b8 b7 b6 b5)MM address should be 13.
⇒ 24 = x + 7 + 5
⇒ x = 12 bit
Now, to map physical memory at 13th set bit (b11 b10 b9 b8 b7 b6 b5)MM address should be 13.
Hence, the correct option is (D).
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Community Answer
A 4-way set-associative cache has lines of 32 byte and a total cache s...
Given Information:
- Cache is 4-way set-associative.
- Each line in the cache is 32 bytes.
- Total cache size is 16 KB.
- Main memory size is 16 MB.
To Find:
Which main memory block is mapped onto set 13 of the cache memory.
Solution:
1. Calculate the number of sets in the cache:
- Cache size = 16 KB = 16,384 bytes
- Line size = 32 bytes
- Number of lines = Cache size / Line size = 16,384 / 32 = 512 lines
- Number of sets = Number of lines / Associativity = 512 / 4 = 128 sets
2. Calculate the number of bits required to represent the set number:
- Number of sets = 128 sets
- 2^x = Number of sets -> 2^x = 128
- Solving for x, we get x = log2(128) = 7 bits
3. Calculate the number of bits required to represent the block offset:
- Line size = 32 bytes
- 2^x = Line size -> 2^x = 32
- Solving for x, we get x = log2(32) = 5 bits
4. Calculate the number of bits required to represent the main memory address:
- Main memory size = 16 MB = 16,777,216 bytes
- 2^x = Main memory size -> 2^x = 16,777,216
- Solving for x, we get x = log2(16,777,216) = 24 bits
5. Calculate the number of bits required to represent the tag:
- Total address bits - Set bits - Block offset bits = 24 - 7 - 5 = 12 bits
6. Determine the set number for the given main memory block:
- Convert the main memory block address to binary: FOA1B5 -> 1111 0000 1010 0001 1011 0101
- Extract the set bits: 0000 01001 1010 0001 1011 0101
- Convert the set bits to decimal: 1001 -> 9
Answer:
The main memory block FOA1B5 is mapped onto set 9 of the cache memory.
- Cache is 4-way set-associative.
- Each line in the cache is 32 bytes.
- Total cache size is 16 KB.
- Main memory size is 16 MB.
To Find:
Which main memory block is mapped onto set 13 of the cache memory.
Solution:
1. Calculate the number of sets in the cache:
- Cache size = 16 KB = 16,384 bytes
- Line size = 32 bytes
- Number of lines = Cache size / Line size = 16,384 / 32 = 512 lines
- Number of sets = Number of lines / Associativity = 512 / 4 = 128 sets
2. Calculate the number of bits required to represent the set number:
- Number of sets = 128 sets
- 2^x = Number of sets -> 2^x = 128
- Solving for x, we get x = log2(128) = 7 bits
3. Calculate the number of bits required to represent the block offset:
- Line size = 32 bytes
- 2^x = Line size -> 2^x = 32
- Solving for x, we get x = log2(32) = 5 bits
4. Calculate the number of bits required to represent the main memory address:
- Main memory size = 16 MB = 16,777,216 bytes
- 2^x = Main memory size -> 2^x = 16,777,216
- Solving for x, we get x = log2(16,777,216) = 24 bits
5. Calculate the number of bits required to represent the tag:
- Total address bits - Set bits - Block offset bits = 24 - 7 - 5 = 12 bits
6. Determine the set number for the given main memory block:
- Convert the main memory block address to binary: FOA1B5 -> 1111 0000 1010 0001 1011 0101
- Extract the set bits: 0000 01001 1010 0001 1011 0101
- Convert the set bits to decimal: 1001 -> 9
Answer:
The main memory block FOA1B5 is mapped onto set 9 of the cache memory.
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A 4-way set-associative cache has lines of 32 byte and a total cache size of 16 KB. Which of the following main memory block is mapped onto the set 13 of the cache memory when 16 MB of main memory is used?a)A295DOb)FCED9Dc)2FAODOd)FOA1B5Correct answer is option 'D'. Can you explain this answer?
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A 4-way set-associative cache has lines of 32 byte and a total cache size of 16 KB. Which of the following main memory block is mapped onto the set 13 of the cache memory when 16 MB of main memory is used?a)A295DOb)FCED9Dc)2FAODOd)FOA1B5Correct answer is option 'D'. 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 A 4-way set-associative cache has lines of 32 byte and a total cache size of 16 KB. Which of the following main memory block is mapped onto the set 13 of the cache memory when 16 MB of main memory is used?a)A295DOb)FCED9Dc)2FAODOd)FOA1B5Correct answer is option 'D'. 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 A 4-way set-associative cache has lines of 32 byte and a total cache size of 16 KB. Which of the following main memory block is mapped onto the set 13 of the cache memory when 16 MB of main memory is used?a)A295DOb)FCED9Dc)2FAODOd)FOA1B5Correct answer is option 'D'. Can you explain this answer?.
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