First, let's calculate the number of blocks in the cache memory:
Number of blocks in cache memory = Cache size / Block size
Number of blocks in cache memory = 2 MB / 256 bytes = 8192 blocks
Next, let's calculate the number of sets in the cache memory for set-associative mapping:
Number of sets = Number of blocks / Associativity
Number of sets = 8192 / 16 = 512 sets
For direct mapping, we need to divide the address into three sub-fields:
Tag + Index + Offset
The tag field identifies which block of main memory the cache block corresponds to. The index field identifies which cache block within the set the data is stored in. The offset field specifies the byte within the cache block where the data is stored.
Tag = log2(Number of blocks in main memory / Block size)
Tag = log2(512 MB / 256 bytes) = 21 bits
Index = log2(Number of cache sets)
Index = log2(512) = 9 bits
Offset = log2(Block size)
Offset = log2(256 bytes) = 8 bits
Therefore, the sub-fields for direct mapping are:
Tag: 21 bits
Index: 9 bits
Offset: 8 bits
For associative mapping, we only need to divide the address into two sub-fields:
Tag + Offset
The tag field identifies which block of main memory the cache block corresponds to. The offset field specifies the byte within the cache block where the data is stored.
Tag = log2(Number of blocks in main memory / Block size)
Tag = log2(512 MB / 256 bytes) = 21 bits
Offset = log2(Block size)
Offset = log2(256 bytes) = 8 bits
Therefore, the sub-fields for associative mapping are:
Tag: 21 bits
Offset: 8 bits
For set-associative mapping, we need to divide the address into three sub-fields:
Tag + Set Index + Offset
The tag field identifies which block of main memory the cache block corresponds to. The set index field identifies which set in the cache the data is stored in. The offset field specifies the byte within the cache block where the data is stored.
Tag = log2(Number of blocks in main memory / Block size)
Tag = log2(512 MB / 256 bytes) = 21 bits
Set Index = log2(Number of sets)
Set Index = log2(512) = 9 bits
Offset = log2(Block size)
Offset = log2(256 bytes) = 8 bits
Therefore, the sub-fields for set-associative mapping are:
Tag: 21 bits
Set Index: 9 bits
Offset: 8 bits
