Consider a set-associative cache of size 2KB (1KB=2^10 bytes) with cache block…
2021
Consider a set-associative cache of size 2KB (1KB=2^10 bytes) with cache block size of 64 bytes. Assume that the cache is byte-addressable and a 32 -bit address is used for accessing the cache. If the width of the tag field is 22 bits, the associativity of the cache is _________ .
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Correct answer: 2
Key facts: Cache size = 2 KB = 2048 bytes; block size = 64 bytes; 32-bit addresses; tag field = 22 bits.
Block offset bits = log2(64) = 6 bits.
Number of cache lines = 2048 / 64 = 32 = 2^5 lines.
If associativity = A, number of sets = 32 / A, so index bits = log2(32/A) = 5 - log2(A).
Tag bits = 32 - index bits - offset bits = 32 - (5 - log2(A)) - 6 = 21 + log2(A).
Set 21 + log2(A) = 22 (given). Therefore log2(A) = 1, so A = 2.
Final answer: The cache is 2-way set-associative.
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