Final answer:
The maximum associativity that a cache with 16-bit addresses, 64-byte cache blocks, and 3-bit tags can support is 64-way, which uses 6 bits for associativity and 1 bit for indexing within the remaining 7 bits of the address not used by the block offset or the tag.
Step-by-step explanation:
Understanding the maximum associativity a cache can support involves knowing how the cache address is structured. Given a cache with 16-bit addresses, 64-byte cache blocks, and 3-bit tags, we can calculate the maximum possible associativity of the cache.
Firstly, let's break down the 16-bit address: the block offset must account for the 64-byte cache blocks, which requires 6 bits (since 26 = 64). Next, considering that the tag is already specified as 3 bits, this leaves us with 7 bits for the index and associativity (16 total bits - 6 bits for block offset - 3 bits for the tag = 7 bits).
The maximum associativity is limited by the number of index bits available in the address. If all 7 bits were used for associativity (meaning no bits were used for indexing), then the cache could be fully associative. However, in that case, the cache would effectively have only one cache line. Therefore, the practical maximum associativity occurs when the index is one bit, resulting in 26 or 64-way associativity because this would leave 6 bits for the associativity field (7 bits for index/associativity - 1 bit for index = 6 bits). Thus, with one index bit, we effectively have 64 sets, and within each set, there could be up to 64 possible slots (ways) to store the cache blocks, considering the 6 bits left for associativity.