Consider two cache organizations: The first one is 32 KB 2-way set associative…
2006
Consider two cache organizations: The first one is 32 KB 2-way set associative with 32-byte block size. The second one is of the same size but direct mapped. The size of an address is 32 bits in both cases. A 2-to-1 multiplexer has a latency of 0.6 ns while a kbit comparator has a latency of k/10 ns. The hit latency of the set associative organization is h1 while that of the direct mapped one is h2. The value of h1 is:
- A.
2.4 ns
- B.
2.3
- C.
1.8
- D.
1.7
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Correct answer: A
Answer: 2.4 ns
Compute cache parameters: 32 KB / 32 B = 1024 blocks.
With 2-way associativity: 1024 / 2 = 512 sets → index = log2(512) = 9 bits.
Block offset = log2(32) = 5 bits.
Tag bits = 32 - index - offset = 32 - 9 - 5 = 18 bits.
Comparator latency = tag bits/10 = 18/10 = 1.8 ns.
For 2-way set associative, add the 2-to-1 multiplexer latency = 0.6 ns.
Total hit latency for set associative (h1) = 1.8 + 0.6 = 2.4 ns.
For reference, hit latency for direct mapped (h2) = comparator latency = 1.8 ns.