---
title: "Convert (430.25)₈ to hexadecimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-430-25-hex"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-430-25-hex
site: BCT Engineering
---

# Convert (430.25)₈ to hexadecimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2076 Chaitra, 1.5 marks
- Video: [Hexadecimal to Binary & Binary to Hexadecimal Conversion](https://www.youtube.com/watch?v=WI6Uvci2p7E) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-430-25-hex
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (430.25)₈ = (?)₁₆.

## Short answer

Convert octal 430.25 to binary as 100011000.010101, regroup bits in fours from the point: 0001 0001 1000 . 0101 0100, giving hex 118.54.

## Answer

Convert octal to binary (3 bits per digit), then regroup the bits in 4s from the binary point (pad with 0s at the ends) to get hex.

**Step 1: Octal to binary**

| Octal | 4 | 3 | 0 | . | 2 | 5 |
|---|---|---|---|---|---|---|
| Binary | 100 | 011 | 000 | . | 010 | 101 |

$(430.25)_8 = (100011000.010101)_2$

**Step 2: Group in 4 bits**

| Groups | 0001 | 0001 | 1000 | . | 0101 | 0100 |
|---|---|---|---|---|---|---|
| Hex | 1 | 1 | 8 | . | 5 | 4 |

Check: $(430.25)_8 = 280.328125_{10}$ and $(118.54)_{16} = 280 + \frac{5}{16} + \frac{4}{256} = 280.328125$.

**Answer:** $(430.25)_8 = (118.54)_{16}$

## Check yourself

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

1. How is octal converted to hex here?
   A. Octal to decimal by division only
   B. Add 3 to each digit
   C. Each octal digit equals a hex digit
   D. Octal to binary (3 bits each), then regroup in 4 bits
   Answer: D. Binary is the common bridge between octal and hex. (Key point: Route)

2. What is (430.25)8 in binary?
   A. 100011000.101010
   B. 011100000.010101
   C. 100011000.010101
   D. 100011.0101
   Answer: C. 4=100, 3=011, 0=000, 2=010, 5=101. (Key point: Binary form)

3. How are bits grouped around the binary point?
   A. In 3s from the left
   B. In 4s from the left end only
   C. In 4s from the point, padding 0s at the ends
   D. In 2s from the point
   Answer: C. Integer part groups leftwards, fraction part rightwards from the point. (Key point: Grouping)

4. What is (430.25)8 in hex?
   A. 118.25
   B. 118.54
   C. 430.54
   D. 11.85
   Answer: B. 0001 0001 1000 . 0101 0100 gives 118.54. (Key point: Result)

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