GATE CS 2016 Set 1 Q32 — Instruction Pipelining

The throughput of a pipeline is determined by its clock cycle time, which is equal to the maximum delay among all the pipeline stages.

1. Original Pipeline

The stage delays are $800$, $500$, $400$, and $300$ picoseconds (ps).

• Original Cycle Time ($T_{\text{old}}$): $$T_{\text{old}} = \max(800, 500, 400, 300) = 800\text{ ps}$$
• Original Throughput ($TP_{\text{old}}$): $$TP_{\text{old}} = \frac{1}{T_{\text{old}}} = \frac{1}{800}\text{ instructions/ps}$$

2. Modified Pipeline

The first stage of $800\text{ ps}$ is replaced by two stages with delays of $600\text{ ps}$ and $350\text{ ps}$. The new set of stage delays is $600$, $350$, $500$, $400$, and $300$ ps.

• New Cycle Time ($T_{\text{new}}$): $$T_{\text{new}} = \max(600, 350, 500, 400, 300) = 600\text{ ps}$$
• New Throughput ($TP_{\text{new}}$): $$TP_{\text{new}} = \frac{1}{T_{\text{new}}} = \frac{1}{600}\text{ instructions/ps}$$

3. Percentage Increase in Throughput

The percentage increase in throughput is calculated as: