---
title: "Convert (1100 0011)Excess-3 to BCD"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-excess3-11000011-bcd"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-excess3-11000011-bcd
site: BCT Engineering
---

# Convert (1100 0011)Excess-3 to BCD

Digital Logic · Chapter 1: Introduction

- Asked in: 2082 Shrawan, 1 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-excess3-11000011-bcd
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (1100 0011)Excess-3 = (?)BCD.

## Short answer

Subtract 0011 from each group: 1100−0011=1001 (9), 0011−0011=0000 (0). The BCD code is (1001 0000).

## Answer

Subtract 3 (0011) from each 4-bit group to get the decimal digit, then write it in BCD.

| XS-3 group | − 3 | Digit | BCD |
|---|---|---|---|
| 1100 (12) | 9 | 9 | 1001 |
| 0011 (3) | 0 | 0 | 0000 |

**Answer: $(1100\ 0011)_{XS-3} = (90)_{10} = (1001\ 0000)_{BCD}$**

## Check yourself

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

1. How do you convert Excess-3 to BCD?
   A. Add 0011 to each group
   B. Invert each group
   C. Subtract 0011 from each 4-bit group
   D. Add 0110 to each group
   Answer: C. The digit is group minus 3. (Key point: Method)

2. 1100 in XS-3 is which digit?
   A. 12
   B. 3
   C. 6
   D. 9
   Answer: D. 1100 = 12 and 12 - 3 = 9. (Key point: First group)

3. What is (1100 0011) XS-3 in BCD?
   A. 1001 0000
   B. 1100 0011
   C. 1001 0011
   D. 0110 0000
   Answer: A. Digits are 9 and 0. (Key point: Final answer)

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