Decimal to Binary Converter

To write a whole number in binary, divide it by 2 again and again until nothing is left, and write down each remainder, 0 or 1. Read from the last remainder to the first, they are the binary number: 13 ÷ 2 = 6, remainder 1; 6 ÷ 2 = 3, remainder 0; 3 ÷ 2 = 1, remainder 1; 1 ÷ 2 = 0, remainder 1, so 13 is 1101. The converter shows exactly these steps for the first number you type, and converts every line at once. It is exact for numbers of any size, and negative numbers keep their minus sign, as in -101 for -5.

For a fraction, the part after the point is multiplied by 2 again and again, and the whole parts are the binary digits: 0.625 × 2 = 1.25 gives 1, 0.25 × 2 = 0.5 gives 0 and 0.5 × 2 = 1 gives 1, so 0.625 is 0.101. Most decimal fractions never end in binary: 0.1 is 0.0(0011), where the digits in brackets repeat forever, which is why computers store 0.1 only approximately. Tick “Group digits” to write the bits in groups of four, “Prefix 0b, 0o or 0x” for 0b1101, and use “From” and “To” for octal, hex or any other base from 2 to 36.