Consider the following processors (ns stands for nanoseconds). Assume that the…
2014
Consider the following processors (ns stands for nanoseconds). Assume that the pipeline registers have zero latency
P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns.
P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns.
P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns.
P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns.
Which processor has the highest peak clock frequency?
- A.
P1
- B.
P2
- C.
P3
- D.
P4
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Correct answer: C
Key insight: the peak clock frequency is limited by the slowest pipeline stage (clock period = maximum stage latency).
P1: stages = 1 ns, 2 ns, 2 ns, 1 ns → slowest = 2 ns → peak frequency = 1 / 2 ns = 0.5 GHz.
P2: stages = 1 ns, 1.5 ns, 1.5 ns, 1.5 ns → slowest = 1.5 ns → peak frequency ≈ 1 / 1.5 ns ≈ 0.667 GHz.
P3: stages = 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns → slowest = 1 ns → peak frequency = 1 / 1 ns = 1.0 GHz.
P4: stages = 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns → slowest = 1.1 ns → peak frequency ≈ 1 / 1.1 ns ≈ 0.909 GHz.
Conclusion: P3 has the highest peak clock frequency (1.0 GHz) because its slowest stage is 1 ns, which is smaller than the slowest stage in the other processors.
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