---
title: "16:1 MUX using 8:1 MUXes"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:mux-16to1-from-8to1"
source: https://www.bctengineer.com/q/semester_3/digital_logic/mux-16to1-from-8to1
site: BCT Engineering
---

# 16:1 MUX using 8:1 MUXes

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2082 Shrawan, 4 marks
- Video: [119 Design of 16  1 Multiplexer using 8  1 Multiplexers](https://www.youtube.com/watch?v=ONRhZooAAUc) — SP Engg. ACADEMY
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/mux-16to1-from-8to1
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

Implement 16:1 multiplexer using only 8:1 multiplexers.

## Short answer

Two 8:1 multiplexers select I0–I7 and I8–I15 using S2,S1,S0. Their outputs feed a third 8:1 mux used as a 2:1 mux: its I0 and I1 get the halves, S3 drives its select, and its other selects are tied to 0. Output Y = S3'P + S3Q.

## Answer

A 16:1 MUX has inputs $I_0$–$I_{15}$ and four selects $S_3S_2S_1S_0$. Using **only 8:1 MUXes**, three are needed:

- **MUX-1 (8:1):** inputs $I_0$–$I_7$, selects $S_2S_1S_0$, output $P$.
- **MUX-2 (8:1):** inputs $I_8$–$I_{15}$, selects $S_2S_1S_0$, output $Q$.
- **MUX-3 (8:1) used as a 2:1 MUX:** $P$ to its $I_0$, $Q$ to its $I_1$; its select $S_0$ is driven by $S_3$ and its other two selects are tied to 0.

```text
         S2 S1 S0
        +--------+
 I0-I7->| MUX-1  |--P--+     +--------+
        +--------+     +---->| I0     |
        +--------+     +---->| I1 MUX3|---> Y
 I8-15->| MUX-2  |--Q--+     | I2-I7=0|
        +--------+           +--------+
         S2 S1 S0            0  0  S3
                             (S2 S1 S0 of MUX-3)
```

$$
Y = S_3'P + S_3Q
$$

| $S_3$ | Y |
|---|---|
| 0 | $P$ = one of $I_0$–$I_7$ |
| 1 | $Q$ = one of $I_8$–$I_{15}$ |

**Example:** $S_3S_2S_1S_0 = 1101$: $P = I_5$, $Q = I_{13}$; MUX-3 select $= 001$ passes $Q$, so $Y = I_{13}$. Correct.

## Check yourself

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

1. How many 8:1 MUXes are needed to build a 16:1 MUX using only 8:1 MUXes?
   A. 2
   B. 4
   C. 3
   D. 5
   Answer: C. Two 8:1 MUXes take the 16 inputs and a third 8:1 MUX acts as a 2:1 MUX to choose between them. (Key point: Number of MUXes)

2. How is the third 8:1 MUX used?
   A. P and Q go to I6 and I7 with S3 on all selects
   B. S3 drives its enable only
   C. All eight inputs carry P and Q alternately and S0 selects
   D. P and Q go to I0 and I1, S3 drives its S0 select and the other selects are tied to 0
   Answer: D. Only select values 000 and 001 are ever used, so I0 = P, I1 = Q and S0 = S3 make it behave as a 2:1 MUX. (Key point: Third MUX usage)

3. What is the output equation of the combined circuit?
   A. Y = S3'P + S3Q
   B. Y = S3P + S3Q
   C. Y = S3' P Q
   D. Y = S2'P + S2Q
   Answer: A. S3 = 0 passes P (from I0-I7) and S3 = 1 passes Q (from I8-I15). (Key point: Output equation)

4. For S3S2S1S0 = 1101, which input reaches Y?
   A. I5
   B. I13
   C. I9
   D. I11
   Answer: B. S2S1S0 = 101 picks I5 in MUX-1 and I13 in MUX-2; S3 = 1 passes Q, so Y = I13. (Key point: Worked example)

## Related in Digital Logic

- [32:1 MUX from 16:1 and 2:1 MUXes](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-32to1-from-16to1) — 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
- [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
- [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
- [Multiplexer tree; 1:16 DEMUX from 1:4](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademux-tree-1to16-from-1to4) — Digital Logic, chapter 4
- [8:1 MUX from 4:1 and 2:1 MUXes](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-8to1-from-4to1-2to1) — Digital Logic, chapter 4

## Related in other subjects

- [Multiplexer and 4:1 MUX](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Amultiplexer-4-1) — Basic Electronics Engineering, chapter 6, asked 2×