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# numpy.invert

`numpy.``invert`(x[, out])

  Compute bit-wise inversion, or bit-wise NOT, element-wise.

  When calculating the bit-wise NOT of an element `x`, each element is first converted to its binary representation (which works just like the decimal system, only now we’re using 2 instead of 10):

  where `W` is the bit-width of the type (i.e., 8 for a byte or uint8), and each is either 0 or 1. For example, 13 is represented as `00001101`, which translates to .

  The bit-wise operator is the result of

  where is the NOT operator, which yields 1 whenever is 0 and yields 0 whenever is 1.

  For signed integer inputs, the two’s complement is returned. In a two’s-complement system negative numbers are represented by the two’s complement of the absolute value. This is the most common method of representing signed integers on computers [40]. A N-bit two’s-complement system can represent every integer in the range to .

  Parameters: | x1 : ndarray Only integer types are handled (including booleans).
  Returns: | out : ndarray Result.

  See also

  `bitwise_and`, `bitwise_or`, `bitwise_xor`, `logical_not`

  `binary_repr`
    Return the binary representation of the input number as a string.

  Notes

  bitwise_not is an alias for invert:

      >>> np.bitwise_not is np.invert
      True

  References

  [40] | Wikipedia, “Two’s complement”, http://en.wikipedia.org/wiki/Two’s_complement

  Examples

  We’ve seen that 13 is represented by `00001101`. The invert or bit-wise NOT of 13 is then:

      >>> np.invert(np.array([13], dtype=uint8))
      array([242], dtype=uint8)
      >>> np.binary_repr(x, width=8)
      '00001101'
      >>> np.binary_repr(242, width=8)
      '11110010'

  The result depends on the bit-width:

      >>> np.invert(np.array([13], dtype=uint16))
      array([65522], dtype=uint16)
      >>> np.binary_repr(x, width=16)
      '0000000000001101'
      >>> np.binary_repr(65522, width=16)
      '1111111111110010'

  When using signed integer types the result is the two’s complement of the result for the unsigned type:

      >>> np.invert(np.array([13], dtype=int8))
      array([-14], dtype=int8)
      >>> np.binary_repr(-14, width=8)
      '11110010'

  Booleans are accepted as well:

      >>> np.invert(array([True, False]))
      array([False,  True], dtype=bool)

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