---
title: "Convert (17)excess-3 to BCD"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-17-excess3-bcd"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-17-excess3-bcd
site: BCT Engineering
---

# Convert (17)excess-3 to BCD

Digital Logic · Chapter 1: Introduction

- Asked in: 2076 Chaitra, 1.5 marks
- Video: [Lec-8: BCD, Excess-3 Code & Conversion with example](https://www.youtube.com/watch?v=UgU5Og9Umak) — Gate Smashers
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-17-excess3-bcd
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (17)excess-3 = (?)BCD.

## Short answer

Assuming decimal 17, its excess-3 is 0100 1010. Subtract 0011 from each nibble to convert to BCD: 0100−0011=0001, 1010−0011=0111 → 0001 0111 (BCD).

## Answer

"17" is not a valid excess-3 bit pattern (XS-3 is written in 4-bit binary groups), so the question is read as: write decimal 17 in excess-3 code and in BCD.

**BCD:** each decimal digit in 4-bit binary.

| Digit | 1 | 7 |
|---|---|---|
| BCD | 0001 | 0111 |

**Excess-3:** each decimal digit + 3, in 4-bit binary.

| Digit | 1 | 7 |
|---|---|---|
| Digit + 3 | 4 | 10 |
| XS-3 | 0100 | 1010 |

Going from XS-3 back to BCD means subtracting 0011 from each group: $0100 - 0011 = 0001$, $1010 - 0011 = 0111$.

**Answer:** $(17)_{10} = (0100\ 1010)_{XS\text{-}3} = (0001\ 0111)_{BCD}$

## Check yourself

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

1. What is 17 in BCD?
   A. 0100 1010
   B. 0001 0111
   C. 10001
   D. 0001 1000
   Answer: B. 1 = 0001 and 7 = 0111. (Key point: BCD of 17)

2. What is 17 in excess-3?
   A. 0001 0111
   B. 0100 1010
   C. 0011 1010
   D. 0100 0111
   Answer: B. 1+3=4 gives 0100 and 7+3=10 gives 1010. (Key point: XS-3 of 17)

3. How do you go from XS-3 back to BCD?
   A. Subtract 0011 from each group
   B. Add 0011 to each group
   C. Complement each group
   D. Shift left
   Answer: A. 0100-0011 = 0001 and 1010-0011 = 0111. (Key point: XS-3 to BCD)

## Related in Digital Logic

- [Convert (1100 0011)Excess-3 to BCD](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-excess3-11000011-bcd) — Digital Logic, chapter 1
- [Convert (1001 1010)excess-3 to BCD](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-excess3-10011010-bcd) — Digital Logic, chapter 1
- [Convert (1010 0111)excess-3 to BCD](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-excess3-10100111-bcd) — Digital Logic, chapter 1
- [Gray→BCD, decimal→Excess-3 and 2's complement addition](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-bcd-excess3-twos-addition) — Digital Logic, chapter 1
- [(1110)gray→BCD and (1430)₁₀→Excess-3](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-to-bcd-decimal-to-excess3) — Digital Logic, chapter 1
- [Digital system advantages; BCD and Excess-3](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Adigital-advantages-bcd-excess3) — Digital Logic, chapter 1

## Related in other subjects

- [8085 ALP: BCD to binary conversion](https://www.bctengineer.com/question.md?key=semester_4%2Fmicroprocessor%3Aalp-8085-bcd-to-binary) — Microprocessor, chapter 2