---
title: "Parallel processing and pipeline speedup"
subject: "Microprocessor"
chapter: 6
key: "semester_4/microprocessor:parallel-processing-pipeline-speedup"
source: https://www.bctengineer.com/q/semester_4/microprocessor/parallel-processing-pipeline-speedup
site: BCT Engineering
---

# Parallel processing and pipeline speedup

Microprocessor · Chapter 6: Advanced Topics

- Asked in: 2069 Poush, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/microprocessor/parallel-processing-pipeline-speedup
- Whole chapter: https://www.bctengineer.com/md/semester_4/microprocessor/chapter-6

## Question

Define parallel processing and show that pipeline can speed up the processing.

## Short answer

Pipelining is a form of parallel processing where instruction execution is divided into k stages. For n tasks, speedup S = (n*k) / (k + n - 1). With large n, S approaches k; e.g., for k=5, n=100, S ≈ 4.81, proving pipelining speeds up processing.

## Answer

#### Parallel processing

Parallel processing means executing more than one task, instruction or part of a problem simultaneously, using multiple processing units or overlapped stages, to get results faster. Pipelining is a form of it.

#### Speed-up by pipelining

Let a task (an instruction) have k stages, each taking one clock time t, and let there be n tasks.

- **Without pipeline:** each task takes k·t, so the total time T₁ = n·k·t.
- **With pipeline:** the first task takes k·t. After that, one task finishes every t. Total time T₂ = (k + n − 1)·t.

Speed-up S = T₁ / T₂ = n·k / (k + n − 1)

For large n, (k + n − 1) ≈ n, so S → **k**. Also S > 1 whenever n > 1 and k > 1, which proves that the pipeline speeds up the processing.

**Example:** k = 5, n = 100:
T₁ = 100 × 5 = 500 t; T₂ = (5 + 99) t = 104 t; S = 500/104 ≈ **4.81**, close to 5.

```text
 Clock:   1  2  3  4  5
 I1       S1 S2 S3
 I2          S1 S2 S3
 I3             S1 S2 S3
 3 stages, 3 instructions:
 time = 3 + 2 = 5 cycles (vs 9 without pipeline)
```

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For n tasks of k stages each with clock time t, the time without a pipeline is:
   A. (k + n - 1)t
   B. n·k·t
   C. k·t
   D. (n + 1)·t
   Answer: B. Each task takes k·t sequentially, so n tasks take n·k·t. (Key point: Time without pipeline)

2. Why is the pipelined time (k + n - 1)t?
   A. The first task takes k·t, then one task completes every t
   B. Every task takes k·t but they all start together
   C. Each task takes t only
   D. The pipeline needs k extra clocks per task
   Answer: A. After the first task finishes in k·t, the remaining n-1 tasks finish one per clock t. (Key point: Time with pipeline)

3. For very large n, the speed-up S = nk/(k + n - 1) approaches:
   A. n
   B. 1
   C. k
   D. n·k
   Answer: C. When n is large, k + n - 1 is about n, so S tends to k, the number of stages. (Key point: Limiting speed-up)

4. For k = 5 stages and n = 100 tasks, the speed-up is about:
   A. 5.00 exactly
   B. 4.81
   C. 20
   D. 1.04
   Answer: B. T1 = 500t, T2 = 104t, so S = 500/104 ≈ 4.81, close to k = 5. (Key point: Worked example)

## Related in Microprocessor

- [8086 speed over 8-bit; major registers](https://www.bctengineer.com/question.md?key=semester_4%2Fmicroprocessor%3A8086-faster-registers) — Microprocessor, chapter 3

## Related in other subjects

- [Pipeline speedup ratio derivation](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Apipeline-speedup-ratio) — Computer Organization and Architecture, chapter 4
- [Parallel pipeline to increase discharge](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aparallel-pipeline-diameter) — Hydro Power, chapter 1
- [Parallel processing and pipelining](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Aparallel-processing) — Computer Organization and Architecture, chapter 4
- [Shunt generator voltage build-up, critical resistance and speed](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-buildup-critical-define) — Electrical Machines I, chapter 3, asked 9×