Convert Decimal to Binary Numbers with Our Free Online Tool

Converting decimal numbers to binary is a fundamental skill in computer science and digital mathematics. Our Decimal to Binary converter makes this process effortless, handling both integers and fractional decimal numbers with precision. Whether you're learning number systems, working on programming assignments, or need quick conversions for technical projects, this tool provides accurate results with optional step-by-step explanations.

The conversion process uses division by 2 for integer parts and multiplication by 2 for fractional parts. Our tool handles complex decimal numbers, including those with repeating binary representations, and can show you exactly how each conversion is performed. This makes it perfect for educational purposes and professional development work.

How to Use the Decimal to Binary Converter

1. Enter Decimal Number: Type your decimal number in the input field. You can enter integers, decimals, or multiple numbers separated by spaces.
2. Configure Options: Choose whether to show conversion steps, handle multiple numbers, limit fractional precision, or validate input format.
3. Convert and Copy: Click "Convert to Binary" to get your result. The tool displays the binary equivalent and optionally shows the complete conversion process.

Frequently Asked Questions About Decimal to Binary

How to convert decimal to binary?

To convert decimal to binary, repeatedly divide the decimal number by 2 and record the remainders. Read the remainders from bottom to top to get the binary result. For example, 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading upward: 1101.

How to change 7 to binary?

To convert 7 to binary: 7 ÷ 2 = 3 remainder 1, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading the remainders from bottom to top gives us 111. Therefore, 7 in binary is 111.

How to convert 12.25 to binary?

To convert 12.25 to binary: First convert 12: 12 = 1100 in binary. Then convert 0.25: 0.25 × 2 = 0.5 (0), 0.5 × 2 = 1.0 (1). So 0.25 = 0.01 in binary. Therefore, 12.25 = 1100.01 in binary.

How do you convert decimals to binary tests?

To convert decimal fractions to binary, multiply the fractional part by 2 repeatedly. If the result is ≥1, write down 1 and subtract 1 from the result. If <1, write down 0. Continue until you get 0 or reach desired precision. For example, 0.375 × 2 = 0.75 (0), 0.75 × 2 = 1.5 (1), 0.5 × 2 = 1.0 (1). So 0.375 = 0.011 in binary.

How to convert 0.1 into binary?

Converting 0.1 to binary: 0.1 × 2 = 0.2 (0), 0.2 × 2 = 0.4 (0), 0.4 × 2 = 0.8 (0), 0.8 × 2 = 1.6 (1), 0.6 × 2 = 1.2 (1), 0.2 × 2 = 0.4 (0)... This creates a repeating pattern. 0.1 in binary is approximately 0.000110011001100... (repeating).