---
title: "Convert (10.0101)₂ to hexadecimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-10-0101-hex"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-10-0101-hex
site: BCT Engineering
---

# Convert (10.0101)₂ to hexadecimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2072 Chaitra, 2 marks
- Video: [How To Convert Binary to Hexadecimal - Computer Science](https://www.youtube.com/watch?v=tSLKOKGQq0Y) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-10-0101-hex
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (10.0101)₂ = (?)₁₆.

## Short answer

Group bits from the binary point: 10 → 0010 (2), .0101 → 0101 (5); result is (2.5)₁₆.

## Answer

Group the bits in fours starting from the binary point: to the left for the integer part and to the right for the fraction, padding with zeros.

```text
 Integer : 10      -> 0010 -> 2
 Fraction: .0101   -> 0101 -> 5
```

Check in decimal: $(10.0101)_2 = 2 + 0.25 + 0.0625 = 2.3125$, and $(2.5)_{16} = 2 + 5/16 = 2.3125$.

**Answer: $(10.0101)_2 = (2.5)_{16}$**

## Check yourself

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

1. How are bits grouped to convert binary to hex?
   A. In fours from the binary point, padding with zeros
   B. In threes from the point
   C. In fours from the left only
   D. In twos from the right
   Answer: A. Each hex digit is 4 bits. (Key point: Grouping rule)

2. What is the integer part 10 binary in hex?
   A. A
   B. 2
   C. 1
   D. 8
   Answer: B. 10 pads to 0010 = 2. (Key point: Integer part)

3. What is (10.0101) binary in hex?
   A. A.5
   B. 2.A
   C. 2.5
   D. 10.5
   Answer: C. Integer 0010 = 2 and fraction 0101 = 5. (Key point: Final answer)

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