About this binary converter
Binary is the base-2 number system computers use, where every digit is a bit that is either 0 or 1. Each position is worth twice the one to its right, so 1101 means 8 + 4 + 0 + 1, which is 13. This converter turns a binary number of up to 128 bits into decimal, hexadecimal, octal, and any other base you pick, using exact big-integer arithmetic. It also splits the bits into nibbles of four, each matching one hex digit, which is the quickest way to read binary by eye, and lists the value of every 1 bit so you can follow the sum.
How to convert binary to decimal
- Enter the binary number. Type 0s and 1s, with or without spaces or a 0b prefix, or press an example.
- Choose an extra base. Pick any base from 2 to 36 under Also convert to, if you need one besides decimal, hex, and octal.
- Press Convert binary. Read the decimal value and the other bases, and copy any of them.
- Check the working. Look at the nibbles and the table of 1 bits to see how the value was built.
Frequently asked questions
How do I convert binary to decimal by hand?
Write the powers of two above the bits from the right: 1, 2, 4, 8, 16, and so on. Add the powers that sit above a 1. For 11010110 that is 128 + 64 + 16 + 4 + 2 = 214.
Why group binary into fours?
Four bits, called a nibble, make exactly one hexadecimal digit from 0 to F. Reading 1101 0110 as D and 6 gives D6 straight away, which is why programmers use hex as shorthand for binary.
Is the binary read as signed or unsigned?
As an unsigned number, so 11111111 is 255, not −1. Put a minus sign in front for a negative value. Two’s complement interpretation is not applied.
What is the largest number I can enter?
Up to 128 binary digits, which is 2 to the power of 128 minus 1, or about 3.4 × 10^38, the size of an IPv6 address or a UUID. Every digit is kept exactly.