Convert Decimal (dec) to Binary (bin)
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Updated on September 1, 2025
You can use our Decimal (dec) to Binary (bin) conversion calculator as a reliable and efficient tool to simplify number conversions. It is designed for professionals, students, and anyone who needs a quick and accurate result. Conversion of Decimal (dec) to Binary (bin) is crucial in Financial systems related measurements. You can avoid the risk of manual calculation errors and save valuable time using our Decimal (dec) to Binary (bin) converter.About Decimal (dec) to Binary (bin) Conversion Calculator
Written By
Nadiba Rahman
Reviewed by
Mrinmoy Roy
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Relation Between Decimal (dec) and Binary (bin)
Let me explain to you about the relation between Decimal dec and Binary (bin) first before moving to the conversion process. Because it’s essential to grasp what these units represent.What is Decimal (dec)?
The decimal number system is a base-10 system, using ten digits (0-9) to represent numbers. Decimal (dec) is a unit of number measurement which is commonly used in Financial systems. The decimal system is the most commonly used number system in everyday life. It is intuitive for humans as it aligns with our natural counting methods using our ten fingers..What is Binary (bin)?
Decimal (dec) is another unit of number measurement that is used in Digital circuits. The binary number system is a base-2 system, using only two digits (0 and 1) to represent numbers.. The decimal system is the most commonly used number system in everyday life. It is intuitive for humans as it aligns with our natural counting methods using our ten fingers..How to Convert Binary (bin)?
The conversion between Decimal (dec) and Binary (bin) follows a simple formula:Binary (bin) = ∑(dₙ×2ⁿ) where dₙ ∈ {0,1} (bin)
Decimal (dec) = ∑(bₙ×2ⁿ) where bₙ ∈ {0,1} (dec)
Where, ∑(dₙ×2ⁿ) where dₙ ∈ {0,1} and ∑(bₙ×2ⁿ) where bₙ ∈ {0,1} is the value that allows you to convert between Decimal (dec) and Binary (bin).
So,
1 Binary = 1 (dec)
And, 1 Decimal = 1 (bin)
Examples of Converting Decimal (dec) to Binary (bin)
To convert any value from Decimal (dec) to Binary (bin), simply multiply the amount of Decimal (dec) by the conversion factor:1 Binary (bin) = 1 Decimal (dec)
For example, if you want to convert 5 Decimal into Binary and the conversion formula is ( ∑(dₙ×2ⁿ) where dₙ ∈ {0,1}), then:
5 Decimal (dec) = 101 Binary (bin)
Decimal (dec) to Binary (bin) Conversion Chart
Here’s a quick reference chart for common conversions between Decimal (dec) and Binary (bin)| Decimal (dec) | Binary (bin) |
|---|---|
| 1 Decimal(dec) | 1 Binary (bin) |
| 5 Decimal(dec) | 101 Binary (bin) |
| 10 Decimal(dec) | 1010 Binary (bin) |
| 15 Decimal(dec) | 1111 Binary (bin) |
| 20 Decimal(dec) | 10100 Binary (bin) |
| 25 Decimal(dec) | 11001 Binary (bin) |
| 30 Decimal(dec) | 11110 Binary (bin) |
| 35 Decimal(dec) | 100011 Binary (bin) |
| 40 Decimal(dec) | 101000 Binary (bin) |
| 45 Decimal(dec) | 101101 Binary (bin) |
How 10 Decimal (dec) Converts to Other number Units
See the relation between Decimal (dec) and other number related measurement units:| 10 Decimal(dec) | 12 Octal (oct) |
| 10 Decimal(dec) | a Hexadecimal (hex) |
Features of Our Decimal (dec) to Binary (bin) Conversion Calculator
Our Decimal dec to Binary (bin) converter is more than just a basic converter. Here's what makes it stand out:Output Precision Control
You can control how precise your conversion results are. From settings, you can adjust decimal places from 0 to 12 places.Customizable Rounding Options
You can control the output rounding options based on your necessity. You can turn the rounding mode on or off, and select between Ceiling or Floor rounding to match your needs.Multiple Number Formats
Display your results the way you want:- Standard format (e.g. 12.345245)
- Scientific notation (e.g. 1.23452e+1)
- Engineering format (e.g. 1.23452 × 10^1)