Number Converters · Browser · Free

Binary to Decimal Converter

Type a binary number to get its value in decimal. The same number is also shown in hexadecimal and octal.

How binary numbers are read

Binary is base 2, so only the digits 0 and 1 appear, and each position stands for a power of 2. Decimal is base 10, where positions step up by tens.

Start at the right-hand end of the binary number. The positions there are 1, 2, 4, 8, 16, 32, 64 and so on, doubling as you move left. The digits that are 1 keep their position value; the digits that are 0 add nothing.

In the number 1010 the two 1s sit under 8 and 2, and the table gives 1010 as 10 in decimal. The same reading gives 11111111 as 255, where every position from 1 up to 128 is filled.

Binary to decimal formula

Write the binary digits in a row, write the values 1, 2, 4, 8, 16 under them from the right, multiply each digit by the value below it, and add the results.

For 1010 the line is 1 x 8 + 0 x 4 + 1 x 2 + 0 x 1, and the table gives that number as 10.

The one field also takes a minus sign in front of the number, a point for a fractional part, and several numbers separated by spaces, which are converted one by one.