To interpret the main memory addresses FF010, 12364, and C7691 considering direct, associative, and 2-way set-associative mapping, we need to first calculate the number of blocks in the cache and the number of sets in the cache for each mapping technique.
Given:
- Main memory size = 1 MB
- Word size = 16 bytes
- Cache size = 64 KB = 2^16 bytes
Therefore, the number of blocks in the cache is:
64 KB / 16 bytes per block = 4,096 blocks
For direct mapping, each block in the main memory is mapped to a unique block in the cache. The mapping is done by dividing the memory address by the number of blocks in the cache and taking the remainder.
- FF010 maps to block 65 (FF010 / 16 = 4063 remainder 2)
- 12364 maps to block 773 (12364 / 16 = 772 remainder 12)
- C7691 maps to block 3953 (C7691 / 16 = 5033 remainder 3)
For associative mapping, each block in the main memory can be mapped to any block in the cache. The cache is searched for the block containing the desired memory address.
- FF010 can be mapped to any block in the cache.
- 12364 can be mapped to any block in the cache.
- C7691 can be mapped to any block in the cache.
For 2-way set-associative mapping, the cache is divided into sets of two blocks each. Each block in the main memory is mapped to a unique set in the cache, and can be placed in either block in the set. The mapping is done by dividing the memory address by the number of sets in the cache and taking the remainder.
- FF010 maps to set 65 (FF010 / 32 = 2031 remainder 18), and can be placed in either block 0 or block 1 in that set.
- 12364 maps to set 386 (12364 / 32 = 386 remainder 12), and can be placed in either block 0 or block 1 in that set.
- C7691 maps to set 247 (C7691 / 32 = 1521 remainder 7), and can be placed in either block 0 or block 1 in that set.
Note that for direct mapping, there can be conflicts if two memory addresses are mapped to the same block in the cache. For 2-way set-associative mapping, conflicts can occur if two memory addresses are mapped to the same set but both blocks in that set are already occupied. In such cases, a replacement algorithm is used to decide which block to evict from the cache to make room for the new block.
