---
title: "Convert (19)₁₀ to Gray"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-19-gray"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-19-gray
site: BCT Engineering
---

# Convert (19)₁₀ to Gray

Digital Logic · Chapter 1: Introduction

- Asked in: 2082 Shrawan, 1 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-19-gray
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (19)₁₀ = (?)Gray.

## Short answer

(19)₁₀ = (10011)₂. Keep MSB and XOR adjacent bits: 1, 1⊕0=1, 0⊕0=0, 0⊕1=1, 1⊕1=0. Result is (11010)Gray.

## Answer

First $(19)_{10} = (10011)_2$ (16 + 2 + 1). Then keep the MSB and XOR adjacent bits:

$G = 1,\ 1\oplus0 = 1,\ 0\oplus0 = 0,\ 0\oplus1 = 1,\ 1\oplus1 = 0$

**Answer: $(19)_{10} = (11010)_{Gray}$**

## Check yourself

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

1. What is 19 decimal in binary?
   A. 11001
   B. 10101
   C. 01101
   D. 10011
   Answer: D. 16 + 2 + 1. (Key point: Decimal to binary)

2. How is a Gray bit formed after the MSB?
   A. XOR of the binary bit and the bit to its left
   B. AND of adjacent bits
   C. Copy of the binary bit
   D. Inversion of the binary bit
   Answer: A. G_i = B_(i+1) XOR B_i. (Key point: Gray rule)

3. What is 19 decimal in Gray?
   A. 10011
   B. 11010
   C. 11001
   D. 10110
   Answer: B. 1; 1^0=1; 0^0=0; 0^1=1; 1^1=0. (Key point: Final answer)

## Related in Digital Logic

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