---
title: "4×4 omega switching network"
subject: "Computer Organization and Architecture"
chapter: 8
key: "semester_5/computer_organization_and_architecture:omega-network"
source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/omega-network
site: BCT Engineering
---

# 4×4 omega switching network

Computer Organization and Architecture · Chapter 8: Multiprocessors

- Asked in: 2073 Chaitra, 4 marks
- Video: [Omega Switching Network | 8x8 Omega Network Construction | Path Contention in Omega Network](https://www.youtube.com/watch?v=4FLyU2oKXzI) — Chirag Bhalodia
- 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/omega-network
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-8

## Question

Design a 4×4 omega switching network and show the switch setting required to connect input 3 to output 1.

## Short answer

A 4×4 omega network has two stages of 2×2 switches, with perfect shuffle connections. To route input 3 (11) to output 1 (01), use destination bits MSB first: stage 1 switch B sets cross (lower input to upper output), stage 2 switch C sets straight (lower input to lower output) to reach Out1.

## Answer

An omega network for N = 4 inputs/outputs has log₂4 = 2 stages, each with N/2 = 2 switches of size 2×2, so 4 switches in total. A **perfect shuffle** (rotate address bits left) connects the inputs to stage 1 and the stage 1 outputs to stage 2.

```text
 In0 -->+-----+--a0------------>+-----+--> Out0
 In2 -->|  A  |--a1-------+      |  C  |--> Out1
        +-----+           |  +-->+-----+
 In1 -->+-----+--b0-------|--+
 In3 -->|  B  |--b1----+  |      +-----+
        +-----+        |  +----->|  D  |--> Out2
                       +-------->|     |--> Out3
                                 +-----+
```
Connections: In0, In2 enter switch A; In1, In3 enter switch B. A's upper output (a0) goes to C's upper input, A's lower output (a1) to D's upper input, B's upper output (b0) to C's lower input, and B's lower output (b1) to D's lower input. Outputs 0, 1 come from C and 2, 3 from D.

#### Routing input 3 (11) to output 1 (01)
Use the destination address bits, MSB first: bit = 0 means the upper output of the switch, bit = 1 means the lower output.

| Stage | Switch | Input used | Destination bit | Output used | Setting |
|---|---|---|---|---|---|
| 1 | B | lower (In3) | 0 (MSB of 01) | upper (b0) | Lower input to upper output (cross) |
| 2 | C | lower (from b0) | 1 (LSB of 01) | lower (Out1) | Lower input to lower output (straight) |

Path: In3 → B (cross) → b0 → C (straight) → Out1. Switches A and D are not used for this connection and can be set arbitrarily.

## Check yourself

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

1. How many 2x2 switches does a 4x4 omega network have?
   A. 8
   B. 4
   C. 2
   D. 16
   Answer: B. log2 4 = 2 stages with N/2 = 2 switches each, so 4. (Key point: Switch count)

2. In omega routing with destination bits, what does bit 0 mean?
   A. Skip the stage
   B. Reset
   C. Lower output of the switch
   D. Upper output of the switch
   Answer: D. 0 = upper output, 1 = lower output, MSB first. (Key point: Routing rule)

3. What are the destination bits for output 1 in a 4x4 network?
   A. 10
   B. 01
   C. 00
   D. 11
   Answer: B. Output 1 is binary 01. (Key point: Output 1)

4. Which path connects input 3 to output 1?
   A. In3 -> A -> a1 -> D -> Out3
   B. In3 -> B -> b0 -> C -> Out1
   C. In3 -> D -> Out0
   D. In3 -> C -> D
   Answer: B. Bit 0 takes the upper output of B (b0), then bit 1 takes the lower output of C (Out1). (Key point: Path)

## Related in Computer Organization and Architecture

- [Crossbar switch vs multistage network](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Acrossbar-vs-multistage) — Computer Organization and Architecture, chapter 8

## Related in other subjects

- [Input/output interface unit design factors](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Aio-interface-unit-importance) — Instrumentation II, chapter 7
- [Time switch and two-stage T-S network](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-switch-two-stage-ts) — Telecommunications, chapter 4
- [Space switch design with connection memory](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-switch-connection-memory) — Telecommunications, chapter 4
- [Time division switching and space switch](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-division-space-switch) — Telecommunications, chapter 4