Decimal To Binary Converter

How To Convert Decimal To Binary Online

The online decimal to binary digit calculator provides an intuitive design that helps users navigate it without any guidelines. Here are the core capabilities of this tool.

Copy & Paste Decimal Numbers in the Input Box

You can directly paste or type decimal values into the input box to begin the conversion process.

Convert Button

Click the “Convert” button to instantly convert the decimal number into binary format.

Reset Button

Use the Reset button to clear the current input and results, so you can start over easily.

File Upload

Upload a file containing decimal values, and the tool will automatically extract and convert them to binary.

Decimal to Binary Calculation Steps

Along with the final binary output, the tool also shows the complete decimal to binary calculation steps. This added feature is helpful for users who want to understand how the result is achieved.

Key Features of SmallSEOTools’ Decimal to Binary Converter

The decimal converter is a valuable asset for its clientele because of its advanced features and benefits. Below are the most prominent ones that make the overall process easier for the users.

• Instantly convert decimal to binary with a single click.
• Displays step-by-step decimal to binary conversion for better learning.
• Upload files for batch processing of multiple decimal numbers.
• A clean, simple interface that requires no effort.
• Accurate results every time, with no need for manual calculation.
• Completely free and accessible from any browser or device.

How to Convert Decimal to Binary Manually with Examples

The conversion process of decimal to binary is not as straightforward as it seems. To convert a decimal to binary, you have to repeatedly divide the decimal number by 2 and record the remainders. All the remainders in reverse order are the required binary equivalent. 

Decimal To Binary Conversion:

Here is an example to depict this whole process.

We will take the decimal number 428.4

428.4 has two parts:

• Integer part = 428
• Fractional part = 0.4

Explanation:

428 ÷ 2 = 214 remainder 0

214 ÷ 2 = 107 remainder 0

107 ÷ 2 = 53 remainder 1

53 ÷ 2 = 26 remainder 1

26 ÷ 2 = 13 remainder 0

13 ÷ 2 = 6 remainder 1

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

So,

428 → 110101100

Fractional part = 0.4

0.4 × 2 = 0.8 → integer part 0

0.8 × 2 = 1.6 → integer part 1

0.6 × 2 = 1.2 → integer part 1

0.2 × 2 = 0.4 → integer part 0

0.4 × 2 = 0.8 → integer part 0

0.8 × 2 = 1.6 → integer part 1

This becomes repetitive, so you can round or stop at some point. Let’s keep 6 bits for simplicity:

0.4 → .011001... (repeating)

Result:

428.4 in binary 110101100.011001

Decimal

Decimal number example:

1037.8125₁₀

= 1×10³ + 0×10² + 3×10¹ + 7×10⁰ + 8×10⁻¹ + 1×10⁻² + 2×10⁻³ + 5×10⁻⁴

Binary

Binary number example:

10000001101.1101₂

= 1×2¹⁰ + 0×2⁹ + 0×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ + 1×2⁻¹ + 1×2⁻² + 0×2⁻³ + 1×2⁻⁴

= 1037.8125₁₀

Decimal to Binary Conversion Table