Turn a binary number into decimal and see every bit do its work, with the answer also shown in octal and hex, exact at any length.
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This binary to decimal converter turns a binary number into its decimal value and shows the working underneath, bit by bit. Each 1 in the input is multiplied by its power of two and the results are added up, so you can follow exactly where the answer came from and check your own working against it.
Type the binary number, read the decimal answer, then check the breakdown.
Binary is a positional system, like decimal, except each place is worth a power of two instead of a power of ten. Reading from the right, the places are worth 1, 2, 4, 8, 16, 32 and so on, doubling each step.
Take 1010. The ones sit in the 8 place and the 2 place, so the value is 8 + 2 = 10. A longer one works the same way: 110011 adds up as 32 + 16 + 2 + 1 = 51. And eight ones in a row, 11111111, give 255, the largest value one byte can hold.
The breakdown matters because most people land here while checking homework or coursework. An answer alone tells you if you were right. The working tells you which bit you misread when you were not.
Under the main answer, the same value also appears in octal and hex. Programmers move between the three all day, since binary gets long to read while hex stays short, and having them side by side saves two extra conversions.
The maths here is exact at any length. Many converters quietly switch to ordinary floating point numbers, which stop being exact past 2 to the power of 53, and long inputs come back subtly wrong. This converter uses arbitrary precision, so a 200-bit number converts digit for digit, with no ceiling of that kind.
Input is checked strictly. A digit that is not 0 or 1 is named on screen, along with its position in the number, instead of the conversion failing with no clue or, worse, quietly dropping the bad digit and answering anyway.
Two limits are stated in the open. The tool converts whole numbers only: if your input has a part after a point, that part is flagged rather than silently thrown away. And a minus sign is handled as sign and magnitude, meaning the answer shows the size of the number with its sign, labelled as such. Two’s complement, the signed format computers store, is not applied here.
Pasted prefixes are handled plainly too. If your binary arrives wearing a 0b prefix, the prefix is stripped and the page tells you it was. The same applies across this converter family for 0x and 0o.
Everything runs in your browser. Your numbers are never uploaded or stored, there is no sign-up, and conversions are unlimited.
Write down the place values from the right: 1, 2, 4, 8, 16 and so on. Add up the values wherever the binary number has a 1. For 1010, that is the 8 place and the 2 place, giving 10.
It is 255. All eight places are filled, so the value is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, which is the largest number a single byte can hold.
Because binary only allows 0 and 1. A stray 2 or a letter usually means a decimal number was pasted by mistake, so the tool names the digit and its position instead of guessing.
No practical one. The conversion uses arbitrary precision maths, so it stays exact far past the 53-bit limit where ordinary calculator maths starts to round.
The whole-number part converts as usual, and the part after the point is flagged on screen. This tool is honest about covering whole numbers only, rather than dropping the fraction without telling you.
Yes, as sign and magnitude: the size converts as normal and the minus sign is carried and labelled. It does not apply two’s complement, which is a storage format rather than a plain value.
Same rules as this one: free, in your browser, with nothing uploaded.
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