---
title: "Convert (1001 1010)excess-3 to BCD"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-excess3-10011010-bcd"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-excess3-10011010-bcd
site: BCT Engineering
---

# Convert (1001 1010)excess-3 to BCD

Digital Logic · Chapter 1: Introduction

- Asked in: 2080 Bhadra, 1.5 marks
- Video: [Excess 3 Code | BCD to Excess 3 code & Vice-versa | Digital logic design | Digital Electronics| STLD](https://www.youtube.com/watch?v=WrHD1roHRKk) — 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/convert-excess3-10011010-bcd
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (1001 1010)excess-3 = (?)BCD.

## Short answer

Subtract 0011 from each excess-3 nibble: 1001₂-0011₂=6, 1010₂-0011₂=7. Decimal 67 is represented in BCD as 0110 0111.

## Answer

Subtract 3 (0011) from each group to get the decimal digit, then write it in BCD.

| XS-3 group | − 3 | Digit | BCD |
|---|---|---|---|
| 1001 (9) | 6 | 6 | 0110 |
| 1010 (10) | 7 | 7 | 0111 |

**Answer: $(1001\ 1010)_{XS-3} = (67)_{10} = (0110\ 0111)_{BCD}$**

## Check yourself

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

1. How to convert XS-3 to BCD?
   A. Subtract 3 from each 4-bit group
   B. Add 3
   C. Invert bits
   D. Shift left
   Answer: A. Group minus 3 gives the digit. (Key point: Method)

2. What digits do 1001 and 1010 represent in XS-3?
   A. 9 and 10
   B. 6 and 7
   C. 4 and 5
   D. 3 and 7
   Answer: B. 9 - 3 = 6; 10 - 3 = 7. (Key point: Digits)

3. What is the BCD?
   A. 1001 1010
   B. 0100 0101
   C. 0110 0111
   D. 0011 0111
   Answer: C. 6 = 0110, 7 = 0111. (Key point: Final answer)

## Related in Digital Logic

- [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
- [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 (17)excess-3 to BCD](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-17-excess3-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