Decimal to Binary Converter

Master Base-10 to Base-2 Conversion

While humans operate in a decimal (Base-10) world, computers store and process data in binary (Base-2). Our Decimal to Binary Converter bridges this gap instantly. It handles standard integers for addressing memory and IP subnets, as well as floating-point numbers (fractions) for precision data analysis.

This tool is built entirely on client-side JavaScript, meaning your calculations happen in your browser—no data is sent to a server. Whether you are a student solving a math problem or a network engineer calculating a subnet mask, this tool ensures speed and privacy.

How it Works

1. Input: Enter your base-10 number. We support negative values and decimals.
2. Configure: Toggle "Show Steps" to see the division-by-2 method for integers and multiplication-by-2 method for fractions.
3. Result: Copy the binary string for use in your code or documentation.

Frequently Asked Questions

How to convert decimal to binary?

Divide the integer by 2 repeatedly and record the remainders (0 or 1). Read the remainders from the last division upwards to the first. For fractions, multiply by 2 repeatedly and record the integer part of the result.

How to change 7 to binary?

7 divided by 2 is 3 remainder 1. 3 divided by 2 is 1 remainder 1. 1 divided by 2 is 0 remainder 1. Reading from bottom to top: 111.

How to convert 12.25 to binary?

Convert 12 (Integer): 1100. Convert 0.25 (Fraction): 0.25 x 2 = 0.5 (0), 0.5 x 2 = 1.0 (1). Combine them: 1100.01.

How do you convert decimals to binary tests?

To convert fractional parts, multiply the decimal by 2. If the result is >= 1, write "1" and subtract 1. If < 1, write "0". Repeat until the fraction reaches 0 or you achieve desired precision.

How to convert 0.1 into binary?

The decimal 0.1 results in a repeating binary fraction. It converts to approximately 0.0001100110011.... This is why floating-point math sometimes results in tiny rounding errors in programming.