---
title: "Convert 37.432 decimal to binary"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-37-432-binary"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-37-432-binary
site: BCT Engineering
---

# Convert 37.432 decimal to binary

Digital Logic · Chapter 1: Introduction

- Asked in: 2074 Chaitra, 3 marks
- Video: [How To Convert Decimal to Binary](https://www.youtube.com/watch?v=rsxT4FfRBaM) — 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-37-432-binary
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert 37.432 decimal number to binary.

## Short answer

Integer 37 by repeated division gives 100101. Fraction 0.432 by repeated multiplication yields about .0110111010. Thus (37.432)₁₀ ≈ (100101.0110111010)₂.

## Answer

Convert the integer and fraction parts separately.

#### Integer part: 37
| Division | Quotient | Remainder |
|---|---|---|
| 37 ÷ 2 | 18 | 1 |
| 18 ÷ 2 | 9 | 0 |
| 9 ÷ 2 | 4 | 1 |
| 4 ÷ 2 | 2 | 0 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |

Reading upwards: $37 = 100101$.

#### Fraction part: 0.432
| Multiplication | Result | Bit |
|---|---|---|
| 0.432 × 2 | 0.864 | 0 |
| 0.864 × 2 | 1.728 | 1 |
| 0.728 × 2 | 1.456 | 1 |
| 0.456 × 2 | 0.912 | 0 |
| 0.912 × 2 | 1.824 | 1 |
| 0.824 × 2 | 1.648 | 1 |
| 0.648 × 2 | 1.296 | 1 |
| 0.296 × 2 | 0.592 | 0 |
| 0.592 × 2 | 1.184 | 1 |
| 0.184 × 2 | 0.368 | 0 |

The fraction does not terminate, so we stop after 10 bits. Reading downwards: $0.432 \approx .0110111010$.

**Answer: $(37.432)_{10} \approx (100101.0110111010)_2$**

Check: $100101.0110111010_2 = 37 + 442/1024 = 37.4316$, very close to 37.432.

## Check yourself

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

1. What is 37 decimal in binary?
   A. 101001
   B. 100101
   C. 100110
   D. 110101
   Answer: B. 37 = 32 + 4 + 1. (Key point: Integer part)

2. How is the fractional part 0.432 converted?
   A. Divide by 2 repeatedly
   B. Multiply by 10
   C. Multiply by 2 repeatedly and read integer parts downward
   D. Read remainders upward
   Answer: C. First bits: 0.864 gives 0, 1.728 gives 1, 1.456 gives 1. (Key point: Fraction method)

3. Why is the binary answer for 37.432 only approximate?
   A. 37 cannot be converted exactly
   B. Binary cannot hold fractions
   C. The integer part overflows
   D. The fraction never terminates, so it is cut after some bits
   Answer: D. 0.432 never reaches zero by repeated doubling. (Key point: Non-termination)

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