---
title: "DEMUX applications; 010 − 011 by 2's complement"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:demux-applications-subtract"
source: https://www.bctengineer.com/q/semester_3/digital_logic/demux-applications-subtract
site: BCT Engineering
---

# DEMUX applications; 010 − 011 by 2's complement

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2081 Baisakh, 2+4 marks
- Video: [Binary Subtraction | 1's | 2's | Complement | Digital logic design | Digital Electronics | STLD | CO](https://www.youtube.com/watch?v=TCGuxRbXU2Q) — Sudhakar Atchala
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/demux-applications-subtract
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

Explain the applications of de-multiplexer. Subtract 011 from 010 using 2's complement method.

## Short answer

A demux routes one data line to a selected output, enabling data distribution, serial-to-parallel conversion, and decoder operation. Subtracting 011 from 010: 2's complement of 011 is 101; adding 010+101=111 with no end carry indicates negative result; its magnitude from 2's complement is 001, so answer -1.

## Answer

#### Applications of a demultiplexer

A demultiplexer sends one input to one of many outputs selected by the select lines. Uses:

- **Data distribution / serial-to-parallel conversion:** serial data on one line is sent to different output lines in turn.
- **Time-division demultiplexing** in communication: separating signals from a shared line at the receiver (e.g. telephone exchanges).
- **Decoder function:** with data input held at 1 (or used as enable), a 1:$2^n$ DEMUX works as an $n$-to-$2^n$ decoder for **memory address decoding** and chip selection.
- **Boolean function generation:** outputs give minterms, which can be ORed to realize functions (e.g. full adder).
- **Control signal routing** in ALUs, microprocessors and multi-display systems.

#### (010)₂ − (011)₂ using 2's complement

Here $010 = 2$ and $011 = 3$; expected result $2 - 3 = -1$.

1. 2's complement of the subtrahend $011$:
   - 1's complement: $100$
   - add 1: $100 + 1 = 101$
2. Add to the minuend:

```text
     010    (+2)
   + 101    (2's complement of 3)
   -----
     111    (no end carry)
```

3. There is **no end carry**, so the result is negative and is in 2's complement form. Take the 2's complement of $111$ to get its magnitude:
   - 1's complement: $000$
   - add 1: $001$

**Answer:** $(010)_2 - (011)_2 = -(001)_2 = (-1)_{10}$. In 3-bit 2's complement form the result is stored as $111$.

## Check yourself

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

1. What does a demultiplexer do?
   A. Selects one of many inputs and sends it to one output
   B. Sends one input to one of many outputs chosen by select lines
   C. Converts a code to one active line without data
   D. Stores a bit
   Answer: B. A DEMUX routes a single data input to one of 2^n outputs. (Key point: DEMUX function)

2. How can a DEMUX act as a decoder?
   A. Connect all outputs together
   B. Remove the select lines
   C. Hold the data input at 1 (or use it as enable) so the selected output goes active
   D. Use a clock on the data input
   Answer: C. With data input = 1, the selected output is 1 for each select code, which is decoder behaviour. (Key point: DEMUX as decoder)

3. What is the 2's complement of 011?
   A. 100
   B. 110
   C. 111
   D. 101
   Answer: D. 1's complement is 100 and adding 1 gives 101. (Key point: 2's complement of 011)

4. After adding 010 + 101 = 111 with no end carry, what is the result?
   A. -1, because no carry means a negative result in 2's complement form
   B. +7, because 111 is 7
   C. +1, because the end carry is dropped
   D. 0, because 111 equals all ones
   Answer: A. No end carry means negative; the 2's complement of 111 is 001, so the answer is -1. (Key point: Result of 010 - 011)

## Related in Digital Logic

- [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
- [De Morgan's theorem and (-47+27) by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademorgan-twos-complement-addition) — Digital Logic, chapter 2
- [DEMUX vs decoder; 4×16 decoder from 2×4](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Adecoder-4x16-from-2x4) — Digital Logic, chapter 4
- [Full adder using decoder; (57−43) by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Afull-adder-decoder-subtract) — Digital Logic, chapter 4
- [FFH AND C0H; (16)₁₀ − (26)₁₀ by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ahex-and-twos-complement-subtract) — Digital Logic, chapter 5

## Related in other subjects

- [2's complement: (1111)2 − (1110)2](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-1111-1110) — Basic Electronics Engineering, chapter 6
- [2's complement: (1111)2 − (1100)2](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-1111-1100) — Basic Electronics Engineering, chapter 6
- [2's complement subtraction; AND using NOR](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-111-110-nor-and) — Basic Electronics Engineering, chapter 6