A cache memory unit with capacity of \(N\) words and block size of \(B\) words…
2017
A cache memory unit with capacity of \(N\) words and block size of \(B\) words is to be designed. If it is designed as a direct mapped cache, the length of the TAG field is 10 bits. If the cache unit is now designed as a 16-way set-associative cache, the length of the TAG field is ____________ bits.
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Correct answer: 14
Key idea: the total address bits and the block offset stay the same, so changing from direct-mapped to 16-way set-associative reduces the number of index bits by log2(16)=4, increasing the tag by the same amount.
For the direct-mapped cache: number of sets = N/B, so index bits = log2(N/B). Block offset bits = log2(B).
For the 16-way set-associative cache: number of sets = (N/B)/16, so index bits = log2(N/B) − log2(16) = log2(N/B) − 4.
Since address size and block offset are unchanged, the tag length increases by 4 bits.
Therefore, new tag length = 10 + 4 = 14 bits.
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