---
title: "Convert (125.25)₁₀ to binary"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-125-25-binary"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-125-25-binary
site: BCT Engineering
---

# Convert (125.25)₁₀ to binary

Digital Logic · Chapter 1: Introduction

- Asked in: 2080 Baisakh, 1.5 marks
- Video: [Lec-2: Convert Decimal to Any Other Base(Binary, Octal, Hex etc) | Number System](https://www.youtube.com/watch?v=M6c6Xw5mt90) — 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-125-25-binary
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (125.25)₁₀ = (?)₂.

## Short answer

Divide 125 by 2 repeatedly: remainders give 1111101. Multiply 0.25 by 2: 0.5 (0), 1.0 (1) yields .01. Result: (1111101.01)₂.

## Answer

Integer: 125 → 62 r1, 31 r0, 15 r1, 7 r1, 3 r1, 1 r1, 0 r1 → read upwards: $1111101$.

Fraction: 0.25 × 2 = 0.5 → 0; 0.5 × 2 = 1.0 → 1 → $.01$.

Check: $64 + 32 + 16 + 8 + 4 + 1 + 0.25 = 125.25$.

**Answer: $(125.25)_{10} = (1111101.01)_2$**

## Check yourself

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

1. 125 in binary?
   A. 1111101
   B. 1110111
   C. 1111011
   D. 1011111
   Answer: A. 64+32+16+8+4+1. (Key point: Integer part)

2. 0.25 in binary?
   A. 0.10
   B. 0.01
   C. 0.11
   D. 0.001
   Answer: B. 0.25 x 2 = 0.5 gives 0; 0.5 x 2 = 1.0 gives 1. (Key point: Fraction part)

3. (125.25) in binary?
   A. 1111101.1
   B. 111101.01
   C. 1111101.01
   D. 1111110.01
   Answer: C. Combine integer and fraction. (Key point: Final answer)

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