Question
15. A non-pipelined system takes 200ns to process a task. The same task can be processed in a 5-segment pipeline with a clock cycle of 40ns. Determine the speedup ratio of the pipeline for 200 tasks. What is the maximum speed-up that could be achieved with the pipeline unit over the non-pipelined unit?
Answer
To the speedup ratio of the pipeline for 200 tasks, we need to compare the total time taken by the non-pipelined system to the total time taken by the pipeline system for processing these tasks.
Non-pipelined system: Total time taken = 200ns × 200 tasks
= 40,000ns
Pipelined system: Clock cycle time = 40ns Number of segments = 5
The pipeline system will have some overhead due to pipeline stalls and startup time. Let's assume that the pipeline has a 10% overhead, which means 10% of the clock cycles are wasted.
Effective clock cycles per task = (1 + overhead) × number of segments
= (1 + 0.1) × 5 = 5.5 clock cycles
Total time taken = clock cycles per task × clock cycle time × number of tasks
= 5.5 × 40ns × 200 tasks = 44,000ns
Speedup ratio = Time taken by non-pipelined system / Time taken by pipeline system
= 40,000ns / 44,000ns ≈ 0.909
Therefore, the speedup ratio of the pipeline for 200 tasks is approximately 0.909.
- To the maximum speed-up that could be achieved with the pipeline unit over the non-pipelined unit, we need to consider the limiting factor. In this case, the limiting factor is the length of the critical path. The critical path is the longest path in the circuit that determines the overall performance.
- In the non-pipelined system, the critical path is 200ns, which is the time taken to process a task.
- In the pipeline system, the critical path is determined by the number of stages and the clock cycle time.
- In this case, the critical path is 5 segments × 40ns = 200ns, which is the time taken for a task to complete one full pipeline stage.
Hence, the maximum speed-up that could be achieved with the pipeline unit over the non-pipelined unit is 200ns (critical path of non-pipelined system) / 200ns (critical path of pipeline system) = 1.
In other words, the maximum speed-up is 1, which means the pipeline system cannot be faster than the non-pipelined system for this particular task.