---
title: "Convert (26.75)₁₀ to binary"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-26-75-binary"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-26-75-binary
site: BCT Engineering
---

# Convert (26.75)₁₀ to binary

Digital Logic · Chapter 1: Introduction

- Asked in: 2080 Bhadra, 1.5 marks
- Video: [Decimal To Binary, Octal, & Hexadecimal Number System conversion in Hindi | CSE GYAN](https://www.youtube.com/watch?v=-gyDAMNyu_Y) — CS Engineering Gyan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-26-75-binary
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (26.75)₁₀ = (?)₂.

## Short answer

Repeatedly divide integer part 26 by 2, reading remainders upward to get 11010; multiply fraction 0.75 by 2, taking integer parts for .11. Combining gives (11010.11)₂.

## Answer

Integer: 26 ÷ 2 = 13 r0, 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1 → read upwards: $11010$.

Fraction: 0.75 × 2 = 1.5 → 1; 0.5 × 2 = 1.0 → 1 → $.11$.

**Answer: $(26.75)_{10} = (11010.11)_2$**

## Check yourself

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

1. What is 26 in binary?
   A. 10110
   B. 11001
   C. 01101
   D. 11010
   Answer: D. 16 + 8 + 2. (Key point: Integer part)

2. What is 0.75 in binary?
   A. 0.11
   B. 0.01
   C. 0.10
   D. 0.101
   Answer: A. 0.75 x 2 = 1.5 gives 1; 0.5 x 2 = 1.0 gives 1. (Key point: Fraction part)

3. In which direction are remainders read in integer conversion?
   A. Downwards
   B. Upwards (last remainder first)
   C. Random
   D. Only the first
   Answer: B. The last remainder is the MSB. (Key point: Method)

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