---
title: "Convert (10011)Gray to octal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-gray-10011-octal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-gray-10011-octal
site: BCT Engineering
---

# Convert (10011)Gray 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-gray-10011-octal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (10011)Gray = (?)₈.

## Short answer

Gray code 10011 converts to binary 11101 (decimal 29) using B_MSB = G_MSB and B_i = B_i+1 XOR G_i. Binary 11101 grouped into 011 101 yields octal 35.

## Answer

Convert Gray to binary, then group the binary in 3 bits for octal.

**Step 1: Gray to binary** ($B_{MSB} = G_{MSB}$, $B_i = B_{i+1} \oplus G_i$)

| Gray bit | Operation | Binary bit |
|---|---|---|
| 1 | copy | 1 |
| 0 | $1 \oplus 0$ | 1 |
| 0 | $1 \oplus 0$ | 1 |
| 1 | $1 \oplus 1$ | 0 |
| 1 | $0 \oplus 1$ | 1 |

$(10011)_{Gray} = (11101)_2 = 29_{10}$

**Step 2: Binary to octal** (group from the right: 011 101)

| Group | 011 | 101 |
|---|---|---|
| Octal | 3 | 5 |

Check: $3 \times 8 + 5 = 29$.

**Answer:** $(10011)_{Gray} = (35)_8$

## Check yourself

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

1. What is (10011) Gray in binary?
   A. 11101
   B. 10011
   C. 10110
   D. 01100
   Answer: A. 1, 1^0=1, 1^0=1, 1^1=0, 0^1=1. (Key point: Step 1)

2. How are binary bits grouped for octal?
   A. In 4s from the right
   B. In 2s from the left
   C. In 3s from the left without padding
   D. In 3s from the right
   Answer: D. 11101 = 011 101. (Key point: Grouping)

3. (10011) Gray in octal?
   A. 23
   B. 53
   C. 29
   D. 35
   Answer: D. 011=3, 101=5; check 3x8+5 = 29 decimal. (Key point: Result)

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