Binary is the base 2 number system computers use, with only two digits, 0 and 1. Each place is a power of two, so 1011 in binary is 8 plus 0 plus 2 plus 1, which equals 11 in our usual base 10 decimal system.

How do I convert decimal to binary?

Divide the decimal number by 2 repeatedly and record the remainders, then read them from bottom to top. This tool does it instantly, and also shows the hexadecimal and octal versions, so you can convert in any direction by typing into the matching box.

What are hexadecimal and octal?

Hexadecimal is base 16, using digits 0 to 9 then A to F, and is common in computing for colours and memory addresses. Octal is base 8, using digits 0 to 7. Both are compact ways to write binary, since each hex digit is four bits and each octal digit is three.

Binary Converter

Convert a number between binary, decimal, hexadecimal, and octal. Type into any box and the others update instantly. It is handy for programming, computer science study, and working with colours, memory, or file permissions. Each system is just a different base for writing the same value.

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Decimal (base 10)

Binary (base 2)

Hexadecimal (base 16)

Octal (base 8)

How number bases work

Every number system uses a base, which is how many digits it has before it rolls over to the next place. Decimal has ten digits, 0 to 9. Binary has two, 0 and 1. Each place is the base raised to a power, so in binary the places are 1, 2, 4, 8, 16 and so on, and you add up the places where there is a 1.

Worked example

The decimal number 42 is 101010 in binary, because 32 plus 8 plus 2 is 42. In hexadecimal it is 2A, since 2 lots of 16 plus 10 is 42, and A stands for 10. In octal it is 52, because 5 lots of 8 plus 2 is 42.

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