---
title: "Convert (11001001)excess-3 to octal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-excess3-11001001-octal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-excess3-11001001-octal
site: BCT Engineering
---

# Convert (11001001)excess-3 to octal

Digital Logic · Chapter 1: Introduction

- Asked in: 2075 Chaitra, 1.5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-excess3-11001001-octal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (11001001)excess-3 = (?)₈.

## Short answer

Excess-3 code 11001001 splits into 1100 (12 - 3 = 9) and 1001 (9 - 3 = 6), giving decimal 96. Decimal 96 converts to octal 140.

## Answer

Decode the excess-3 groups to decimal (subtract 3 from each group), then convert decimal to octal.

**Step 1: XS-3 to decimal**

| XS-3 group | 1100 | 1001 |
|---|---|---|
| Value | 12 | 9 |
| Minus 3 | 9 | 6 |

So the number is $96_{10}$.

**Step 2: Decimal to octal**

| Division | Quotient | Remainder |
|---|---|---|
| 96 ÷ 8 | 12 | 0 |
| 12 ÷ 8 | 1 | 4 |
| 1 ÷ 8 | 0 | 1 |

Bottom to top: 140. Check: $1 \times 64 + 4 \times 8 + 0 = 96$.

**Answer:** $(11001001)_{XS\text{-}3} = (96)_{10} = (140)_8$

## Check yourself

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

1. What do you do to XS-3 groups?
   A. Add 3
   B. Complement them
   C. Subtract 3 from each group
   D. Group them in 3s
   Answer: C. XS-3 = digit + 3. (Key point: XS-3 decode)

2. What decimal is (1100 1001) XS-3?
   A. 129
   B. 96
   C. 63
   D. 99
   Answer: B. 12-3=9 and 9-3=6. (Key point: Decimal)

3. 96 in octal?
   A. 140
   B. 160
   C. 104
   D. 114
   Answer: A. 96 = 1x64 + 4x8 + 0. (Key point: Octal)

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