---
title: "Convert (93)₁₀ to Excess-3"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-93-excess3"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-93-excess3
site: BCT Engineering
---

# Convert (93)₁₀ to Excess-3

Digital Logic · Chapter 1: Introduction

- Asked in: 2072 Chaitra, 2 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-93-excess3
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (93)₁₀ = (?)Excess-3.

## Short answer

Add 3 to each decimal digit: 9 → 1100, 3 → 0110; Excess-3 result is 1100 0110.

## Answer

In Excess-3 code each decimal digit is coded separately as the 4-bit binary of (digit + 3).

| Digit | Digit + 3 | Excess-3 |
|---|---|---|
| 9 | 12 | 1100 |
| 3 | 6 | 0110 |

**Answer: $(93)_{10} = (1100\ 0110)_{XS-3}$**

## Check yourself

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

1. How is each digit coded in Excess-3?
   A. 4-bit binary of the digit
   B. 4-bit binary of (digit - 3)
   C. 4-bit binary of (digit + 3)
   D. 3-bit binary of the digit
   Answer: C. Add 3 to each digit separately. (Key point: XS-3 rule)

2. What is the Excess-3 code of 9?
   A. 1001
   B. 1011
   C. 0110
   D. 1100
   Answer: D. 9 + 3 = 12 = 1100. (Key point: Digit 9)

3. What is (93) decimal in Excess-3?
   A. 1100 0110
   B. 1001 0011
   C. 1100 0011
   D. 0110 1100
   Answer: A. 9 gives 1100 and 3 gives 0110, in order. (Key point: Final answer)

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