Decimal to Binary Converter

This tool turns any whole decimal number into binary, and shows the division by 2 working
underneath so you can see exactly how each remainder built the result. Type a number, get the binary
value back immediately, and expand the working panel any time you want to check it by hand.

How to convert decimal to binary

  1. Type your whole decimal number into the input box.
  2. The tool divides it by 2, keeps the remainder, and carries the quotient into the next division.
  3. It repeats that division until the quotient reaches 0.
  4. Reading the remainders from the last one back to the first gives the binary result, expand the working panel to see every step in order.

How decimal becomes binary

Converting decimal to binary works by dividing repeatedly by 2 and keeping track of what is left over each time. Once the quotient hits 0, reading the remainders backward gives the binary number. Here is decimal 11 worked through step by step.

Division step

Quotient

Remainder

11 divided by 2

5

1

5 divided by 2

2

1

2 divided by 2

1

0

1 divided by 2

0

1

Reading the remainders from bottom to top, 1, 1, 0, 1, gives 1011. So decimal 11 equals binary 1011, matching the same pair used on the Binary to Decimal Converter, just approached from the other direction.

Breaking a number down this way is not a new idea. Egyptian scribes were multiplying by repeated doubling more than 3,600 years ago. The Rhind Mathematical Papyrus, copied by the scribe Ahmes around 1650 BCE, shows numbers being multiplied by splitting one factor into powers of 2, which historians studying the text describe as an early, practical use of binary thinking, centuries before anyone wrote the number system down formally.

Who ends up using this converter

Who

Why they land here

Students and learners

Checking a decimal to binary homework answer, or working out the method for the first time.

Programmers and hobbyists

Needing a quick binary literal for code, a config value, or a small embedded project, without doing the division by hand.

Binary to Decimal Converter and Binary Calculator

Binary to Decimal Converter

Turns binary digits into a base 10 number, the reverse of this page.

Binary Calculator

Handles full binary arithmetic beyond a single conversion, addition, subtraction, multiplication, and division, each with its decimal equivalent shown alongside.

Last updated September 2026. Every conversion here runs standard, checkable division by 2 math. See the Binary Code Glossary for any term on this page you are not sure about.

Frequently Asked Questions

This page converts a whole base 10 number into binary using repeated division by 2. The Binary to Decimal Converter runs the opposite process, multiplying each binary digit by its position value and adding the results.

Divide the number by 2 and write down the remainder, then keep dividing the quotient by 2 until it reaches 0. Reading the remainders backward, from the last one to the first, gives the binary number. The worked example above shows this for decimal 11.

Not this one, it handles whole numbers only. Fractional decimals convert to binary with a different method, repeated multiplication by 2 rather than division, which the Decimal to Binary Conversion Guide walks through separately.

This converter works with positive whole numbers. Negative values are represented in binary through two’s complement, a different encoding, see our Two’s Complement Explained guide for how that works.

No practical limit for everyday use, the tool converts numbers well beyond the range of a standard 32 bit or 64 bit integer without losing accuracy.

The first remainder you calculate lines up with the smallest place value, and the last one lines up with the largest, so reading them from last to first puts the digits in the correct order for the final binary number.