---
title: "Convert (1010 0111)excess-3 to BCD"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-excess3-10100111-bcd"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-excess3-10100111-bcd
site: BCT Engineering
---

# Convert (1010 0111)excess-3 to BCD

Digital Logic · Chapter 1: Introduction

- Asked in: 2079 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-excess3-10100111-bcd
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (1010 0111)excess-3 = (?)BCD.

## Short answer

Subtract 0011 from each 4-bit group: 1010-0011=0111 (7), 0111-0011=0100 (4). Result: (0111 0100)BCD.

## Answer

**Rule:** an excess-3 (XS-3) code word is the BCD code of each decimal digit plus 3 (0011). So subtract 0011 from each 4-bit group to get the BCD digit.

| XS-3 group | Value | Subtract 3 | BCD |
|---|---|---|---|
| 1010 | 10 | 10 − 3 = 7 | 0111 |
| 0111 | 7 | 7 − 3 = 4 | 0100 |

So the decimal number is 74.

**Answer:** $(1010\ 0111)_{XS\text{-}3} = (0111\ 0100)_{BCD}$ (= $74_{10}$).

## Check yourself

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

1. How is an excess-3 group turned into BCD?
   A. Subtract 0011 (3) from each 4-bit group
   B. Add 0011 to each group
   C. Subtract 0110 from each group
   D. Complement each group
   Answer: A. XS-3 is BCD plus 3, so subtract 3. (Key point: XS-3 to BCD rule)

2. What decimal digit does XS-3 group 1010 represent?
   A. 10
   B. 3
   C. 13
   D. 7
   Answer: D. 1010 = 10 and 10 - 3 = 7. (Key point: First group)

3. What is (1010 0111) XS-3 in BCD?
   A. 1010 0111
   B. 0100 0111
   C. 0111 0100
   D. 0111 0111
   Answer: C. Digits are 7 and 4, i.e. decimal 74. (Key point: Final result)

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