---
title: "Short note: MUX tree"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:short-note-mux-tree"
source: https://www.bctengineer.com/q/semester_3/digital_logic/short-note-mux-tree
site: BCT Engineering
---

# Short note: MUX tree

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2081 Baisakh, 2 marks
- Video: [MUX Tree: Design, Structure, Implementation, and Solved Examples in Digital Electronics](https://www.youtube.com/watch?v=ss9oF45_JUQ) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/short-note-mux-tree
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

Write a short note on MUX tree.

## Short answer

A MUX tree builds a large multiplexer by cascading smaller MUXes: lower select bits drive the first level, whose outputs feed higher-select-bit MUXes. For example, an 8:1 MUX uses seven 2:1 MUXes. It uses standard ICs but adds delay.

## Answer

A **MUX tree** is a way of building a large multiplexer from several smaller multiplexers connected in levels (a tree). It is used when a single IC with enough inputs is not available.

- The first level of small MUXes receives the data inputs. The lower-order select lines are applied to all of them in common.
- The outputs of the first level go to the data inputs of the next level, which is driven by the higher-order select lines.
- The last MUX gives the final output $Y$.

**Example: 8:1 MUX from 2:1 MUXes** (needs 4 + 2 + 1 = 7 MUXes):

```text
I0,I1 -[2:1]-+
I2,I3 -[2:1]-+-[2:1]-+
I4,I5 -[2:1]-+       +-[2:1]--> Y
I6,I7 -[2:1]-+-[2:1]-+
      ^S0       ^S1     ^S2
```

Similarly a 16:1 MUX can be built from five 4:1 MUXes (four in the first level using $S_1S_0$, one in the second level using $S_3S_2$).

**Advantages:** large MUX from standard small ICs; easy to expand. **Drawback:** more ICs and more propagation delay (one MUX delay per level).

## Check yourself

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

1. Why is a MUX tree used?
   A. To build a large MUX from smaller standard MUXes when no IC with enough inputs exists
   B. To increase speed
   C. To reduce the number of ICs
   D. To store data
   Answer: A. Standard small ICs are combined in levels to make a bigger multiplexer. (Key point: Purpose)

2. Which select lines drive the first level of the tree?
   A. The highest-order selects
   B. The lower-order selects, applied in common
   C. Different selects for each MUX
   D. No selects, only enables
   Answer: B. The first level uses the lower selects and the last MUX uses the higher selects. (Key point: Select line assignment)

3. How many 2:1 MUXes build an 8:1 MUX?
   A. 3
   B. 4
   C. 7
   D. 8
   Answer: C. 4 + 2 + 1 = 7. (Key point: MUX count)

## Related in Digital Logic

- [Short note: DE-MUX tree](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ashort-note-demux-tree) — Digital Logic, chapter 4
- [32:1 MUX tree; implement Σm(0,1,3,8,9,13,15)](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-32to1-tree-function-15) — Digital Logic, chapter 4
- [32:1 MUX tree from 4:1; implement Σ(0,1,3,8,9,13)](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-32to1-tree-function) — Digital Logic, chapter 4
- [Multiplexer tree; 16:1 MUX from 4:1](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-16to1-from-4to1) — Digital Logic, chapter 4