I would appreciate it if you could Please provide answers instead of \"pointing

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I would appreciate it if you could Please provide answers instead of "pointing in the right direction" I can go to Google for that or my textbook or pay a local tu tor. But am paying money here on Chegg for this, so kindly understand. Thanks in advance.
Q: A two-way set associative cache organization consists of two direct mapped caches where a cache line in each one stores a block of eight words and a tag. The combined cache memory can accommodate a total of 512 words from main memory (excluding the tags). The main memory size is 256K x 16.

What is the tag size for each block of words stored in the cache?

What is the size of each individual direct-mapped cache? Give your answer in address space x addressability form.

Explanation / Answer

Size of Main Memory, Smain = 256K x 16 = 512KB

Assuming size of word is 2 Bytes,

Scache = 512x2 = 1024 Bytes

From the question, the memory has word addressability, so,

Sword = 2 Bytes

Associativity, A = 2

Size of Tag (in Bytes), Stag = log2 ((Smain x A) / (Scache x Sword))

Stag = log2 ((512x1024x2)/(1024x2))

Stag = log2(512)

Stag = 9 Bytes

Both caches combined can occupy a total of 512 words. This implies individual cache occupies 256 words each. 1 tag for 8 words implies 32 tags for 256 words.

So, size of each cache = (32x9B) +256 words

= 16x9 words + 256 words

= 400 x 16 (including tags)

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