Why does ~True result in -2?
The Python bool
type is a subclass of int
(for historical reasons; booleans were only added in Python 2.3).
Since int(True)
is 1
, ~True
is ~1
is -2
.
See PEP 285 for why bool
is a subclass of int
.
If you wanted the boolean inverse, use not
:
>>> not True
False
>>> not False
True
If you wanted to know why ~1
is -2
, it's because you are inverting all bits in a signed integer; 00000001
becomes 1111110
which in a signed integer is a negative number, see Two's complement:
>>> # Python 3
...
>>> import struct
>>> format(struct.pack('b', 1)[0], '08b')
'00000001'
>>> format(struct.pack('b', ~1)[0], '08b')
'11111110'
where the initial 1
bit means the value is negative, and the rest of the bits encode the inverse of the positive number minus one.
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.
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
~True == -2
is not surprising if True
means 1
and ~
means bitwise inversion...
...provided that
True
can be treated as an integer and- integers are represented in Two's complement
Edits:
- fixed the mixing between integer representation and bitwise inversion operator
- applied another polishing (the shorter the message, the more work needed)