# Why Does “~True” Result in -2 in Python?

In this short article, I’ll try to explain why we get the following:

`$ python3`

Python 3.9.0 (default, Dec 6 2020, 18:02:34)

[Clang 12.0.0 (clang-1200.0.32.27)] on darwin

Type "help", "copyright", "credits" or "license" for more information.

>>> ~True

-2

Think about `bool`

, you'll find that it is **numeric** in nature - It can hold two values, "True" and "False", and they are just ‘customized’ versions of the integers 1 and 0, that only print themselves differently.

So now it’s clear that `bool`

is actually a subclass of `int`

:

>>> type(True)

<class 'bool'>

>>> isinstance(True, int)

True>>> True == 1

True

>>> True is 1 # they're still different objects

False

Having that said, `~True`

evaluates to:

`~True == ~int(True) == ~1 == -2`

The `~`

operator is for bitwise inversion — it simply flips bits. So:

`1 = 00000001`

~1 = 11111110

which is -2 in two’s complement. The ‘algorithm’ below describes how to get a number’s two’s complement:

- Flip all the bits
- add 1 to the resulting number
- interpret the result as a binary representation of the magnitude
- to determine the sign — if the original number begins with ‘1’, it’s negative, positive otherwise

`11111110 → 00000001 → 00000010 `

↑ ↑

Flip Add 1

“00000010” in binary is 2, but since the original number is “11111110”, which its MSB is “1”, the sign is determined as negative, and the final result would be “-2”.

I hope that was clear :)