Here is the question: A direct-mapped cache consists of 8 blocks. A byte-addressable main memory contains 4K blocks of eight bytes each. Access time for the cache is 20 ns and the time required to fill a cache slot from main memory is 300 ns. Assume a request is always started in sequential to cache and then to main memory. If a block is missing from cache, the entire block is brought into the cache and the access is restarted. Initially, the cache is empty. b) Compute the hit ratio for a program that loops 3 times from address 0 to 75 (base 10) in memory. For b, another example has been provided in regards to a previous problem: A direct-mapped cache consists of eight blocks. Main memory contains 4K blocks of eight words each. Access time for the cache is 22 ns and the time required to fill a cache slot from main memory is 300ns (this time will allow us to determine the block is missing and bring it into cache). Assume a request is always started in parallel to both cache and to main memory (so if it is not found in cache, we do not have to add this cache search time to the memory access). If a block is missing from cache, the entire block is brought into the cache and the access is restarted. Initially, the cache is empty. b. Compute the hit ratio for a program that loops 4 times from locations 0 to 67(base10) in memory. This was the answer: Block 0 of main memory (addresses 0 - 7) and Block 8 of main memory (addresses 64 - 67) must share a cache block. The remaining blocks are brought in and are not replaced. So for each access to Block 0, there is one miss and 7 hits. For each access to Block 8, there is one miss and 3 hits. The remaining blocks have one miss each, with all other accesses being hits. If we loop 4 times, we have: Block 0: 4 misses, 28 hits Block 1: 1 miss, 31 hits Block 2: 1 miss, 31 hits Block 3: 1 miss, 31 hits Block 4: 1 miss, 31 hits Block 5: 1 miss, 31 hits Block 6: 1 miss, 31 hits Block 7: 1 miss, 31 hits Block 8: 4 misses, 12 hits for a total of 15 misses, 257 hits, or a hit ratio of 94.49%. In a similar manner, can you show how the misses and hits are being calculated for my question with 0-75 base 10 and the different times as well. Detailed explanations are appreciated and please no chatGPT as those questions are incorrect. thanks!
Here is the question:
A direct-mapped cache consists of 8 blocks. A byte-addressable main memory contains 4K blocks of eight bytes each. Access time for the cache is 20 ns and the time required to fill a cache slot from main memory is 300 ns. Assume a request is always started in sequential to cache and then to main memory. If a block is missing from cache, the entire block is brought into the cache and the access is restarted. Initially, the cache is empty.
b) Compute the hit ratio for a program that loops 3 times from address 0 to 75 (base 10) in memory.
For b, another example has been provided in regards to a previous problem: A direct-mapped cache consists of eight blocks. Main memory contains 4K blocks of eight words each. Access time for the cache is 22 ns and the time required to fill a cache slot from main memory is 300ns (this time will allow us to determine the block is missing and bring it into cache). Assume a request is always started in parallel to both cache and to main memory (so if it is not found in cache, we do not have to add this cache search time to the memory access). If a block is missing from cache, the entire block is brought into the cache and the access is restarted. Initially, the cache is empty.
b. Compute the hit ratio for a program that loops 4 times from locations 0 to 67(base10) in memory.
This was the answer:
Block 0 of main memory (addresses 0 - 7) and Block 8 of main memory (addresses 64 - 67) must share a cache block. The remaining blocks are brought in and are not replaced. So for each access to Block 0, there is one miss and 7 hits. For each access to Block 8, there is one miss and 3 hits. The remaining blocks have one miss each, with all other accesses being hits.
If we loop 4 times, we have:
Block 0: 4 misses, 28 hits
Block 1: 1 miss, 31 hits
Block 2: 1 miss, 31 hits
Block 3: 1 miss, 31 hits
Block 4: 1 miss, 31 hits
Block 5: 1 miss, 31 hits
Block 6: 1 miss, 31 hits
Block 7: 1 miss, 31 hits
Block 8: 4 misses, 12 hits for a total of 15 misses, 257 hits, or a hit ratio of 94.49%.
In a similar manner, can you show how the misses and hits are being calculated for my question with 0-75 base 10 and the different times as well. Detailed explanations are appreciated and please no chatGPT as those questions are incorrect. thanks!
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