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

This tool converts a number between decimal, binary, hexadecimal and octal at the same time, so you see one value written in every base without doing the working by hand. Type a number into any of the four boxes, decimal, binary, hex or octal, and the other three update instantly to show the matching value, because all four are different ways of writing the same underlying number. If you enter something invalid for that base, such as a 2 in the binary box, the tool flags it with an error message rather than showing a wrong result, and it warns you if a number is too large to convert accurately. This is handy for programming and computer science study, where binary and hexadecimal show up constantly in memory addresses, colour codes and low-level data, and where octal is still used for file permissions on Unix systems. The page also explains how place value works in each base, since every number system is built the same way, with digits representing powers of the base rather than powers of ten, and it walks through a worked example showing how the decimal number 42 becomes 101010 in binary, 2A in hexadecimal and 52 in octal. Use it to check manual conversions, translate a hex colour or memory address into decimal, or build a feel for how the four systems relate.

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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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