---
title: "DEMUX vs decoder; seven-segment \"b\" segment"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:demux-decoder-b-segment"
source: https://www.bctengineer.com/q/semester_3/digital_logic/demux-decoder-b-segment
site: BCT Engineering
---

# DEMUX vs decoder; seven-segment "b" segment

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2081 Bhadra, 2+2+3 marks
- Video: [Seven Segment Display Decoder (Part 2)](https://www.youtube.com/watch?v=_qGFpgpqf7s) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/demux-decoder-b-segment
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

Compare a demultiplexer with the decoder. What is a seven-segment decoder? Find out the simplest logic expression for "b" segment of the BCD to 7-segment display decoder and realize the circuit.

## Short answer

A demultiplexer routes one data input to a selected output, while a decoder activates one output line for a given code. Segment b expression: b = B' + (C XNOR D). Realize with an inverter, an XNOR gate, and an OR gate.

## Answer

#### DEMUX vs decoder

A **demultiplexer** sends one data input to one of $2^n$ outputs chosen by $n$ select lines. A **decoder** converts an $n$-bit input code into one active line out of $2^n$ lines. A decoder with an enable input works as a DEMUX if the enable is used as the data input.

| Point | Demultiplexer | Decoder |
|---|---|---|
| Inputs | 1 data + n select | n code inputs (+ enable) |
| Function | Routes data to a chosen line | Activates the line for a code |
| Output content | Copy of the data bit | Fixed 1 (or 0) on one line |
| Use | Data distribution, serial-to-parallel | Address decoding, code conversion |
| Example | 1:8 DEMUX | 3-to-8 decoder (74138) |

#### Seven-segment decoder

A **BCD-to-seven-segment decoder** (e.g. 7447/7448) takes a 4-bit BCD digit $ABCD$ and produces seven outputs $a$ to $g$ that light the segments of an LED display so that the decimal digit 0–9 is shown. Inputs 1010–1111 never occur, so they are don't-cares.

```text
     a
    ---
 f | g | b
    ---
 e |   | c
    ---
     d
```

#### Simplest expression for segment "b"

Segment b is ON for digits 0, 1, 2, 3, 4, 7, 8, 9 and OFF for 5 and 6 (standard 7447 style).

$$
b = \Sigma m(0,1,2,3,4,7,8,9) + d(10,11,12,13,14,15)
$$

K-map (rows AB, columns CD):

| AB \ CD | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | 1 | 1 | 1 | 1 |
| 01 | 1 | 0 | 1 | 0 |
| 11 | X | X | X | X |
| 10 | 1 | 1 | X | X |

Groups: rows 00 and 10 (all $B=0$) give $B'$; column 00 gives $C'D'$; column 11 gives $CD$.

$$
b = B' + C'D' + CD = B' + (C \odot D)
$$

#### Circuit

```text
 B ---[NOT]--- B' ---------+
                           +--[OR]--- b
 C --+                     |
     +--[XNOR]--- C⊙D -----+
 D --+
```

So segment b needs one inverter, one XNOR and one 2-input OR gate (or with AND/OR: $C'D'$ and $CD$ from two AND gates and a 3-input OR).

## Check yourself

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

1. Which is correct about a demultiplexer?
   A. It has n code inputs and no data input
   B. It routes one data input to one of 2^n outputs selected by n select lines
   C. It always outputs a fixed 1 on one line
   D. It combines many inputs into one
   Answer: B. A demux copies the data bit to the chosen output, while a decoder just activates the line for a code. (Key point: DEMUX vs decoder)

2. How can a decoder with enable work as a DEMUX?
   A. Use the enable as the data input
   B. Tie all inputs high
   C. Use outputs as selects
   D. It cannot
   Answer: A. The data goes to the enable, and the code inputs act as select lines. (Key point: Decoder as DEMUX)

3. What does a BCD-to-seven-segment decoder do?
   A. Converts a 4-bit BCD digit into signals a–g lighting the display
   B. Converts 7 bits to BCD
   C. Adds BCD digits
   D. Selects one of 7 inputs
   Answer: A. It drives the seven segments so the decimal digit 0–9 is displayed; inputs 10–15 are don't-cares. (Key point: Seven-segment decoder)

4. What is the simplest expression for segment b?
   A. B' + C ⊙ D
   B. B + C ⊙ D
   C. B' + C ⊕ D
   D. A + B'
   Answer: A. Groups give B', C'D' and CD, and C'D' + CD is the XNOR. (Key point: Segment b expression)

## Related in Digital Logic

- [BCD-to-seven-segment decoder, segments a and e](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Abcd-seven-segment-a-e) — Digital Logic, chapter 4
- [Seven-segment decoder "b" segment](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ab-segment-seven-segment) — Digital Logic, chapter 4, asked 2×
- [Seven-segment "a" segment using NOR gates](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aa-segment-nor-gates) — Digital Logic, chapter 4
- [BCD-to-7-segment decoder; frequency counter](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Abcd-7segment-frequency-counter) — Digital Logic, chapter 11
- [Seven-segment "e" segment](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ae-segment-seven-segment) — Digital Logic, chapter 4
- [Seven-segment "b" and "d" segments](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ab-d-segments) — Digital Logic, chapter 4

## Related in other subjects

- [BCD counter 0-9999 on seven segment VHDL](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Avhdl-bcd-counter-seven-segment) — Embedded System, chapter 9
- [Display 99 to 00 on seven segment](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3A8051-seven-segment-99-00) — Embedded System, chapter 9
- [Seven segment display and clock counter](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aseven-segment-clock-design) — Embedded System, chapter 9
- [Display 0 to 9 on seven segment](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3A8051-seven-segment-0-9) — Embedded System, chapter 9, asked 2×