Bit length

This calculator finds the bit length of an input integer. It also displays the number of digits required to represent the number in other forms (decimal, octal, hex). It also shows the input number representation in these forms.

Big integer bit length

Big integer number

Calculate

Bit count

89

Binary form

11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

Octal digits

30

Octal form

377777777777777777777777777777

Decimal digits

27

Decimal form

618970019642690137449562111

Hex digits

23

Hex code

1ffffffffffffffffffffff

Byte count

12

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The calculator has no limits on input length, it actually depends on your system memory resources. For example a 1000-digits number can be entered as

Bit length calculation algorithms

The calculator finds out the number of binary digits by converting an input number to string form and calculating its length. In real applications, this method is inefficient. To implement bit length calculation effectively, one must know the number representation method in a particular computer environment and the cost of math and bitwise operations calculating.
E.g. a number bit length can be calculated by rounding the binary logarithm operation result to the nearest larger integer: