Free Online Decimal to Binary Converter

How to convert decimal to binary

Convert decimal numbers to binary instantly: type a value and the binary result appears as you type. Below the converter you'll find the method to do it by hand, a worked example and a table of common values.

1. Type or paste a decimal number into the box above. Negative numbers and fractions work too.
2. The From and To bases are already set to decimal and binary, so the result appears right away: 156 becomes 10011100.
3. Copy the result, or choose any other base from 2 to 60 to convert the same value.

Converting decimal to binary by hand

Divide the number by 2 and write down the remainder. Keep dividing the result by 2 until it reaches 0. The remainders, read from the last one to the first, are the binary digits. To check the answer, multiply each digit by its place value and add them up:

10011100₂ = 1·2⁷ + 0·2⁶ + 0·2⁵ + 1·2⁴ + 1·2³ + 1·2² + 0·2¹ + 0·2⁰
= 128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156₁₀

Decimal to binary table

Decimal and binary explained

Decimal is base 10, the everyday number system with the digits 0 to 9. Each position is worth ten times the one to its right.

Binary is base 2: it uses only the digits 0 and 1, and each position is worth twice the one to its right. It is how computers store every number, character and pixel.