---
title: "Convert (329.54)₁₀ to hexadecimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-329-54-hex"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-329-54-hex
site: BCT Engineering
---

# Convert (329.54)₁₀ to hexadecimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2079 Bhadra, 1.5 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-329-54-hex
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (329.54)₁₀ = (?)₁₆.

## Short answer

Divide 329 by 16 to get 149; multiply 0.54 by 16 repeatedly to get 8, A, 3, D, 7. Result: (149.8A3D7)₁₆ (approx).

## Answer

**Integer part:** 329 ÷ 16 = 20 r 9; 20 ÷ 16 = 1 r 4; 1 ÷ 16 = 0 r 1 → $(149)_{16}$.

**Fraction part** (multiply by 16):

| Step | Result | Digit |
|---|---|---|
| 0.54 × 16 | 8.64 | 8 |
| 0.64 × 16 | 10.24 | A |
| 0.24 × 16 | 3.84 | 3 |
| 0.84 × 16 | 13.44 | D |
| 0.44 × 16 | 7.04 | 7 |

The fraction does not terminate, so we stop at 5 digits.

**Answer: $(329.54)_{10} \approx (149.8A3D7)_{16}$**

## Check yourself

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

1. How is the integer part 329 converted to hex?
   A. Repeated division by 16, reading remainders bottom to top
   B. Repeated multiplication by 16
   C. Repeated division by 8
   D. Repeated division by 10
   Answer: A. Integer parts are divided by the base, and the remainders read from last to first give the digits. (Key point: Integer part method)

2. What is (329)10 in hex?
   A. 941
   B. 1A9
   C. 14A
   D. 149
   Answer: D. 329 = 20x16+9, 20 = 1x16+4, so the digits are 1, 4, 9 giving 149. (Key point: Integer result)

3. How is the fractional part 0.54 converted?
   A. Repeatedly divide it by 16
   B. Multiply by 10 and read the remainders
   C. Repeatedly multiply the fraction by 16 and take the integer parts in order
   D. Convert it like the integer part
   Answer: C. Fractions are multiplied by the base, and the integer parts top to bottom form the hex fraction. (Key point: Fraction method)

4. In 0.64 x 16 = 10.24, which hex digit is written?
   A. 10
   B. D
   C. A
   D. 2
   Answer: C. The integer part 10 is written A in hex. (Key point: Digit 10 in hex)

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