---
title: "1×16 DMUX using 1×4 DMUX"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:demux-1x16-from-1x4"
source: https://www.bctengineer.com/q/semester_3/digital_logic/demux-1x16-from-1x4
site: BCT Engineering
---

# 1×16 DMUX using 1×4 DMUX

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2076 Asoj, 3 marks
- Video: [U2L5.3 | 1:16 Demultiplexer using 1:4 Demux | 1 X16 Demux Using 1 X 4 Demux |1:4 Demux to 1:16 Demux](https://www.youtube.com/watch?v=3yl02STV1H0) — Techno Tutorials ( e-Learning)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/demux-1x16-from-1x4
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

Realize the logic circuit of 1×16 DMUX using 1×4 DMUX and gates if necessary.

## Short answer

Use five 1×4 demuxes in a tree. The first demux uses select bits S3S2 to route data D to one of four second-level demuxes, which use S1S0 to select the final output from Y0–Y15. No extra gates needed.

## Answer

A 1×16 DMUX needs 4 select lines $S_3S_2S_1S_0$. It is built as a **demultiplexer tree** from five 1×4 DMUXes; no extra gates are needed.

- **Stage 1:** one 1×4 DMUX receives the data $D$ and uses the MSBs $S_3S_2$ to send it to one of four second-stage DMUXes.
- **Stage 2:** four 1×4 DMUXes use $S_1S_0$ and produce $Y_0$–$Y_{15}$.

```text
                       S1 S0
                     +------+-- Y0..Y3
         S3 S2    +->| DM1  |
       +------+   |  +------+
  D -->| DM0 0|---+  +------+-- Y4..Y7
       |     1|----->| DM2  |
       |     2|---+  +------+
       |     3|-+ |  +------+-- Y8..Y11
       +------+ | +->| DM3  |
                |    +------+
                |    +------+-- Y12..Y15
                +--->| DM4  |
                     +------+
```

| $S_3S_2$ | Active stage-2 DMUX | Outputs reached by $S_1S_0$ |
|---|---|---|
| 00 | DM1 | $Y_0$–$Y_3$ |
| 01 | DM2 | $Y_4$–$Y_7$ |
| 10 | DM3 | $Y_8$–$Y_{11}$ |
| 11 | DM4 | $Y_{12}$–$Y_{15}$ |

Example: $S = 1110$ → DM0 picks DM4, DM4 picks its output 2, so $D$ appears at $Y_{14}$.

## Check yourself

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

1. How many 1x4 DEMUXes are needed to build a 1x16 DEMUX?
   A. Four
   B. Five
   C. Eight
   D. Sixteen
   Answer: B. One DEMUX at stage 1 and four at stage 2 give 4 x 4 = 16 outputs. (Key point: Number of DEMUXes)

2. Which select bits drive the first-stage DEMUX?
   A. S1 S0
   B. S3 S2
   C. S3 S0
   D. S2 S1
   Answer: B. The MSBs S3S2 choose the group; S1S0 then choose the output within the group at stage 2. (Key point: Select bit use)

3. For S3S2S1S0 = 1110, at which output does D appear?
   A. Y14
   B. Y12
   C. Y11
   D. Y6
   Answer: A. S3S2 = 11 picks DM4 (Y12-Y15), and S1S0 = 10 picks its output 2, which is Y14. (Key point: Worked example)

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