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Consider 4-block cache (initially empty) with the following main memory block references:
4,5,7,12,4,5,13,4,5,7
Identify the hit ratio for direct-mapped cache?
4,5,7,12,4,5,13,4,5,7
Identify the hit ratio for direct-mapped cache?
Correct answer is '0.3'. Can you explain this answer?
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Most Upvoted Answer
Consider 4-block cache (initially empty) with the following main memor...
Direct-mapped Cache
In a direct-mapped cache, each block of main memory can be mapped to only one specific location in the cache. This mapping is determined by the address of the block modulo the number of cache blocks.
Given Information
- Cache size: 4 blocks
- Main memory block references: 4, 5, 7, 12, 4, 5, 13, 4, 5, 7
Cache Initialization
The cache is initially empty, so all cache blocks are invalid.
Cache Operation
1. Block 4:
- Cache: Empty
- Miss: Block 4 is fetched from main memory and placed in cache block 0.
2. Block 5:
- Cache: [4, -, -, -]
- Miss: Block 5 is fetched from main memory and placed in cache block 1.
3. Block 7:
- Cache: [4, 5, -, -]
- Miss: Block 7 is fetched from main memory and placed in cache block 3.
4. Block 12:
- Cache: [4, 5, -, 7]
- Miss: Block 12 is fetched from main memory and placed in cache block 0, replacing block 4.
5. Block 4 (again):
- Cache: [12, 5, -, 7]
- Hit: Block 4 is found in cache block 0.
6. Block 5 (again):
- Cache: [12, 4, -, 7]
- Hit: Block 5 is found in cache block 1.
7. Block 13:
- Cache: [12, 4, 5, 7]
- Miss: Block 13 is fetched from main memory and placed in cache block 2, replacing block 5.
8. Block 4 (again):
- Cache: [12, 13, 5, 7]
- Miss: Block 4 is fetched from main memory and placed in cache block 0, replacing block 12.
9. Block 5 (again):
- Cache: [4, 13, -, 7]
- Miss: Block 5 is fetched from main memory and placed in cache block 2, replacing block 5.
10. Block 7 (again):
- Cache: [4, 13, 5, -]
- Hit: Block 7 is found in cache block 3.
Hit Ratio Calculation
The hit ratio is calculated by dividing the number of cache hits by the total number of memory references.
Number of cache hits: 3 (block 4, 5, 7)
Total memory references: 10
Hit ratio = Number of cache hits / Total memory references = 3 / 10 = 0.3
Therefore, the hit ratio for the direct-mapped cache is 0.3, or 30%.
In a direct-mapped cache, each block of main memory can be mapped to only one specific location in the cache. This mapping is determined by the address of the block modulo the number of cache blocks.
Given Information
- Cache size: 4 blocks
- Main memory block references: 4, 5, 7, 12, 4, 5, 13, 4, 5, 7
Cache Initialization
The cache is initially empty, so all cache blocks are invalid.
Cache Operation
1. Block 4:
- Cache: Empty
- Miss: Block 4 is fetched from main memory and placed in cache block 0.
2. Block 5:
- Cache: [4, -, -, -]
- Miss: Block 5 is fetched from main memory and placed in cache block 1.
3. Block 7:
- Cache: [4, 5, -, -]
- Miss: Block 7 is fetched from main memory and placed in cache block 3.
4. Block 12:
- Cache: [4, 5, -, 7]
- Miss: Block 12 is fetched from main memory and placed in cache block 0, replacing block 4.
5. Block 4 (again):
- Cache: [12, 5, -, 7]
- Hit: Block 4 is found in cache block 0.
6. Block 5 (again):
- Cache: [12, 4, -, 7]
- Hit: Block 5 is found in cache block 1.
7. Block 13:
- Cache: [12, 4, 5, 7]
- Miss: Block 13 is fetched from main memory and placed in cache block 2, replacing block 5.
8. Block 4 (again):
- Cache: [12, 13, 5, 7]
- Miss: Block 4 is fetched from main memory and placed in cache block 0, replacing block 12.
9. Block 5 (again):
- Cache: [4, 13, -, 7]
- Miss: Block 5 is fetched from main memory and placed in cache block 2, replacing block 5.
10. Block 7 (again):
- Cache: [4, 13, 5, -]
- Hit: Block 7 is found in cache block 3.
Hit Ratio Calculation
The hit ratio is calculated by dividing the number of cache hits by the total number of memory references.
Number of cache hits: 3 (block 4, 5, 7)
Total memory references: 10
Hit ratio = Number of cache hits / Total memory references = 3 / 10 = 0.3
Therefore, the hit ratio for the direct-mapped cache is 0.3, or 30%.
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Community Answer
Consider 4-block cache (initially empty) with the following main memor...
Cache Memory is a special very high-speed memory. It is used to speed up and synchronize with a high-speed CPU. Cache memory is costlier than main memory or disk memory but more economical than CPU registers. Cache memory is an extremely fast memory type that acts as a buffer between RAM and the CPU. It holds frequently requested data and instructions so that they are immediately available to the CPU when needed.
The performance of cache memory is frequently measured in terms of a quantity called hit ratio.
{K MOD N = i}
4 − M;4 MOD 4 = 0
5 − M;5 MOD 4 = 1
7 − M;7 MOD 4 = 3
12 − M;12 MOD 4 = 0
4 − M;4 MOD 4 = 0
5 − H
13 − M;13 MOD 4 = 1
4 − H
5 − M;5 MOD 4 = 1
7 − H
⇒ H = 3/10
= 0.3
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Consider 4-block cache (initially empty) with the following main memory block references:4,5,7,12,4,5,13,4,5,7Identify the hit ratio for direct-mapped cache?Correct answer is '0.3'. Can you explain this answer?
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