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Binary to decimal converter
Type or paste a binary number and read its decimal value at once. Spaces between groups are ignored, and with Signed turned on the bits are read as a two's complement value.
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How it works
Type the numberEnter the value in the input box. Spaces and underscores between digits are ignored.
See the resultThe converted value appears right away, together with the other common bases.
Copy itPress Copy next to the result you need.
Reading binary numbers
Each binary digit is worth twice the digit on its right: 1, 2, 4, 8, 16 and so on. Add up the values of the positions that hold a 1 and you have the decimal number. 11111101010 is 1024 + 512 + 256 + 128 + 64 + 32 + 8 + 2 = 2026.
Bit patterns from registers, network packets or file headers are often signed. With Signed on, 11111111 in 8 bits reads as -1 instead of 255, and the unsigned value is shown next to it. Binary fractions such as 0.101 are supported too and convert to 0.625. Paste numbers with spaces or underscores between groups; they are ignored.
Frequently asked questions
Is 11111111 equal to 255 or -1?
Both, depending on how it is read. As an unsigned 8 bit value it is 255; as a signed two's complement value it is -1. Turn on Signed to see the second reading.
How do I convert decimal to binary by hand?
Divide the number by 2 again and again and write down the remainders, then read them from the last to the first. For 13: 13, 6, 3, 1 give remainders 1, 0, 1, 1, so 13 is 1101.
Why does 0.1 never end in binary?
Because 1/10 cannot be written as a sum of powers of two, just as 1/3 never ends in decimal. The repeating part 0011 is shown in brackets.
What is the largest number I can convert?
Numbers with up to 20,000 digits are accepted. The results are exact, there is no rounding.