---
title: "Arithmetic pipeline with example"
subject: "Computer Organization and Architecture"
chapter: 4
key: "semester_5/computer_organization_and_architecture:arith-pipeline"
source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/arith-pipeline
site: BCT Engineering
---

# Arithmetic pipeline with example

Computer Organization and Architecture · Chapter 4: Pipeline & Vector Processing

- Asked in: 2074 Asoj, 6 marks; 2069 Asar, 6 marks (asked 2 times)
- Video: [Arithmetic Pipeline || Computer Organization Architecture || Pipelining](https://www.youtube.com/watch?v=Q6rdSDKn544) — Sudhakar Atchala
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/arith-pipeline
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-4

## Question

Explain arithmetic pipeline with an example.

## Short answer

Arithmetic pipeline divides an operation like floating-point addition into segments (compare exponents, align mantissas, add, normalise). Example: X=0.9504×10³ and Y=0.8200×10²; after alignment to 0.0820×10³, sum 1.0324×10³ normalises to 0.10324×10⁴. n additions take k+n-1 clocks.

## Answer

An arithmetic pipeline divides an arithmetic operation (such as floating-point addition or multiplication) into sub-operations, with each one done in its own segment. Different pairs of numbers are in different segments at the same time, so after the first result a new result comes out every clock cycle. It is used in high-speed floating-point units and vector processors.

#### Example: floating-point addition pipeline (4 segments)
Segments, with registers R between them:
1. Compare the exponents
2. Align the mantissas (shift the smaller number)
3. Add or subtract the mantissas
4. Normalise the result (and adjust the exponent)

```text
 Exponents a,b        Mantissas A,B
     |                    |
 [Compare exponents]------+   R
     v                    v
 [Choose exponent, align mantissa]   R
                  v
         [Add/subtract mantissas]    R
                  v
       [Normalise, adjust exponent]  R
                  v
                result
```

Numerical example: X = 0.9504 × 10³ and Y = 0.8200 × 10².
1. Exponents: 3 and 2, difference = 1, so the larger exponent 3 is chosen.
2. Align: Y = 0.0820 × 10³.
3. Add: 0.9504 + 0.0820 = 1.0324 × 10³.
4. Normalise: 0.10324 × 10⁴.

Result Z = 0.10324 × 10⁴ (= 1032.4). Check: 950.4 + 82.0 = 1032.4.

With 4 segments of equal time, n additions take (4 + n - 1) clocks instead of 4n.

## Check yourself

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

1. Order of FP addition segments?
   A. Compare exponents, align mantissas, add, normalise
   B. Add, align, compare, normalise
   C. Normalise, add, compare, align
   D. Align, compare, normalise, add
   Answer: A. Matches the 4-segment design. (Key point: Segments)

2. In X=0.9504x10^3, Y=0.8200x10^2, Y after align?
   A. 0.8200 x 10^3
   B. 0.0820 x 10^3
   C. 8.200 x 10^2
   D. 0.0082 x 10^3
   Answer: B. Shift smaller by exponent difference 1. (Key point: Align)

3. Clocks for n additions?
   A. 4n
   B. n
   C. n+1
   D. 4 + n - 1
   Answer: D. Versus 4n non-pipelined. (Key point: Time)

## Related in Computer Organization and Architecture

- [Arithmetic and instruction pipeline](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Aarith-instr-pipeline) — Computer Organization and Architecture, chapter 4, asked 2×
- [How arithmetic pipeline increases performance](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Aarith-pipeline-performance) — Computer Organization and Architecture, chapter 4