Why does ~True result in -2?

Question

In Python console:

~True

Gives me:

-2

Why? Can someone explain this particular case to me in binary?

Answer 1

int(True) is 1.

1 is:

00000001

and ~1 is:

11111110

Which is -2 in Two's complement¹

¹ Flip all the bits, add 1 to the resulting number and interpret the result as a binary representation of the magnitude and add a negative sign (since the number begins with 1):

11111110 → 00000001 → 00000010 
         ↑          ↑ 
       Flip       Add 1

Which is 2, but the sign is negative since the MSB is 1.

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Worth mentioning:

Think about bool, you'll find that it's numeric in nature - It has two values, True and False, and they are just "customized" versions of the integers 1 and 0 that only print themselves differently. They are subclasses of the integer type int.

So they behave exactly as 1 and 0, except that bool redefines str and repr to display them differently.

>>> type(True)
<class 'bool'>
>>> isinstance(True, int)
True

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