16. A non-pipeline system takes 100ns to process a task. The same task can be processed in a 5-stage pipeline with a clock cycle of 20ns. Determine the speedup ratio of the pipeline for 100 tasks. What is the theoretical speedup that could be achieved with the pipeline system over a non-pipelined system?
To speedup ratio of the pipeline system over the non-pipelined system, we can compare the time taken by each system to process the same number of tasks. Let's consider 100 tasks in this case.
Non-pipeline system: Time per task = 100ns Total time for 100 tasks = 100 tasks * 100ns = 10000ns = 10μs
Pipeline system: Clock cycle time = 20ns Number of pipeline stages = 5
The time taken for a single task in the pipeline system can be calculated by adding the clock cycle time for each stage: Time per task in pipeline system = Number of pipeline stages * Clock cycle time = 5 * 20ns = 100ns
Total time for 100 tasks in the pipeline system = 100 tasks * 100ns = 10000ns = 10μs
Speedup ratio = Time taken by non-pipeline system / Time taken by pipeline system Speedup ratio = 10μs / 10μs = 1
Hence, the speedup ratio of the pipeline system for 100 tasks is 1. This indicates that the pipeline system processes the tasks at the same rate as the non-pipelined system.
The theoretical speedup that could be achieved with the pipeline system over a non-pipelined system can be calculated using the formula:
Theoretical Speedup = Number of pipeline stages
In this case, the theoretical speedup would be 5 (as there are 5 pipeline stages). This represents the maximum potential speedup that can be achieved by pipelining the system compared to a non-pipelined system with the given number of stages.