# Bit length

The calculator counts number of bits required to represent a number in the binary form. It also displays an input number in binary, octal, decimal, and hex forms.

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

Bit count

Binary form

Octal digits

Octal form

Decimal digits

Decimal form

Hex digits

Hex code

Byte count

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

123E1000

### 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:
$\lceil log_2{(x+1)} \rceil$

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