# class Bignum < Integer

`Bignum` objects hold integers outside the range of `Fixnum`. `Bignum` objects are created automatically when integer calculations would otherwise overflow a `Fixnum`. When a calculation involving `Bignum` objects returns a result that will fit in a `Fixnum`, the result is automatically converted.

For the purposes of the bitwise operations and `[]`, a `Bignum` is treated as if it were an infinite-length bitstring with 2's complement representation.

While `Fixnum` values are immediate, `Bignum` objects are not—assignment and parameter passing work with references to objects, not the objects themselves.

## instance methods

Arithmetic operations
Performs various arithmetic operations on big.
 big `+` aNumeric Addition big `-` aNumeric Subtraction big `*` aNumeric Multiplication big `/` aNumeric Division big `%` aNumeric Modulo big `**` aNumeric Exponentiation
Bit operations
Performs various operations on the binary representations of the `Bignum`.
 `~` big Invert bits big `|` aNumeric Bitwise OR big `&` aNumeric Bitwise AND big `^` aNumeric Bitwise EXCLUSIVE OR big `<<` aNumeric Left-shift aNumeric bits big `>>` aNumeric Right-shift aNumeric bits (with sign extension)
<=>
big <=> aNumeric → -1, 0, +1
Comparison—Returns -1, 0, or +1 depending on whether big is less than, equal to, or greater than aNumeric. This is the basis for the tests in `Comparable`.
[ ]
big[ n ] → 0, 1
Bit Reference—Returns the nth bit in the (assumed) binary representation of big, where big is the least significant bit.
```a = 9**15 50.downto(0) do |n| print a[n] end```

produces:

`000101110110100000111000011110010100111100010111001`
size
big.size → anInteger
Returns the number of bytes in the machine representation of big.
```(256**10 - 1).size → 12 (256**20 - 1).size → 20 (256**40 - 1).size → 40```
to_f
big.to_f → aFloat
Converts big to a `Float`. If big doesn't fit in a `Float`, the result is infinity.
to_i
big.to_i → big
Returns big.
to_s
big.to_s → aString
Returns a string containing the decimal representation of big. 