Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage…
2016
Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies \(τ_1, τ_2\), and \(τ_3\) such that \(τ_1 = 3τ_2/4 = 2τ_3\). If the longest pipeline stage is split into two pipeline stages of equal latency, the new frequency is ___________ GHz, ignoring delays in the pipeline registers.
Answer: 4 — Answer: 4 GHz Compute the original clock period from the given 3 GHz frequency: Torig = 1 / 3 GHz = 1/3 ns ≈ 0.333... ns. Use the stage relations. From τ1 =…
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Correct answer: 4
Answer: 4 GHz
Compute the original clock period from the given 3 GHz frequency: Torig = 1 / 3 GHz = 1/3 ns ≈ 0.333... ns.
Use the stage relations. From τ1 = (3/4) τ2 and τ1 = 2 τ3, we get τ2 is the longest stage, so Torig = τ2.
Find numerical values relative to Torig = τ2 = 1/3 ns:
τ1 = (3/4)·τ2 = (3/4)·(1/3 ns) = 1/4 ns = 0.25 ns.
τ3 = τ1 / 2 = 0.25 ns / 2 = 0.125 ns.
After splitting the longest stage into two equal parts, each split stage has latency τ2/2 = (1/3 ns)/2 = 1/6 ns ≈ 0.1667 ns.
The new clock period is the maximum of the stage latencies after the split: max(τ1, τ2/2, τ3) = max(0.25 ns, 0.1667 ns, 0.125 ns) = 0.25 ns.
Therefore the new frequency is 1 / 0.25 ns = 4 GHz (ignoring pipeline register delays).
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