Final answer:
For cache memory with direct mapping, the address format consists of a tag field (5 bits), a block field (8 bits), and a word field (5 bits), determined by the main memory size, cache size, and block size.
Step-by-step explanation:
The question pertains to computer memory, specifically how address formats are determined for cache memory under direct mapping conditions. The addresses are divided into different fields to identify particular words within memory blocks. An address would generally consist of a tag, a block (or index), and a word field. For this example:
- Main memory size = 8K blocks (which means 8192 blocks as 1K=1024 blocks)
- Cache memory size = 256 blocks
- Block size = 32 words
In direct mapping, each block of main memory maps to only one possible cache line.
The block or index field is used to determine which cache line a memory block will map to. The size of the block field can be determined by the number of cache blocks, which is 256 in this case, requiring 8 bits (since 28 = 256).
The word field identifies which word in the block is being referred to, and given that each block has 32 words, we need 5 bits to represent this (since 25 = 32).
The tag field comprises the remaining bits of the address. If we have 8K blocks in main memory and 256 blocks in the cache, we have 8192/256 = 32 blocks in main memory for each block in cache, requiring an additional 5 bits for the tag (since 25 = 32).
Therefore, the address format for the cache memory under direct mapping would be: Tag (5 bits), Block (8 bits), Word (5 bits).