Ones Complement Calculator

How it is calculated

The one's complement of a binary number is made by inverting every bit: each 0 becomes 1 and each 1 becomes 0. The tool takes the digits exactly as typed, so the width is the number of characters you enter, and leading zeros are kept and flipped. It returns the flipped string, the bit count, and the decimal value of the original number, Σ bi × 2i, where bi is the bit at position i counted from the right. The decimal figure is computed with exact digit arithmetic, so even a 67-bit input of all ones shows 147,573,952,589,676,412,927. For an n-bit input the complement equals (2n − 1) − value. The input may contain only 0 and 1 and be at most 2048 digits long: spaces, a 0b prefix, other digits or an empty field give no result.

Common mistakes

• Confusing one's complement with two's complement. Two's complement is the one's complement plus 1, so the two give different answers for every number.
• Dropping the leading zeros. 00101100 and 101100 are different widths, and their complements, 11010011 and 010011, are different too.
• Typing a prefix or separators such as 0b1011 or 1011 0010. Only the digits 0 and 1 are accepted, so remove them first or there is no result.
• Entering a decimal number or hexadecimal digits. The input is read as binary only, so a value like 44 returns no result.
• Treating the output as the negative of the number in everyday arithmetic. In a signed one's-complement system it represents the negative, but the tool only flips bits and does not interpret the sign.