# Calculating Speedup Ratio of Pipelined System for 15 Tasks

## What is the speedup ratio of a pipelined system compared to a non-pipelined system for 15 tasks?

The speedup ratio of the pipeline for 15 tasks is 5 / 8.

## Understanding Speedup Ratio Calculation

**Speedup ratio** is a measure of how much faster a new system can complete tasks compared to an old system.

In the given scenario, a non-pipelined system takes 20 ns to process a single task, while the same task can be processed in a 16-segment pipeline with a clock cycle of 2 ns. This results in a speedup ratio of 5/8 for 15 tasks.

Now, let's calculate the time taken by both systems to complete 15 tasks:

- Time taken in a non-pipelined system: 15 tasks x 20 ns = 300 ns
- Time taken in a pipelined system: Each task takes 16 cycles * 2 ns/cycle = 32 ns; 15 tasks x 32 ns = 480 ns

By comparing the time taken by both systems, we can calculate the speedup ratio as follows:

**Speedup ratio = Time taken by non-pipelined system / Time taken by pipelined system = 300 ns / 480 ns = 5 / 8**

Therefore, the speedup ratio of the pipeline for 15 tasks is 5 / 8, indicating that the pipelined system is 5/8 times faster than the non-pipelined system for processing 15 tasks.