The binary representation of False is 0000000000000000 (how many bits are used depends on the implementation). If you perform a binary NOT operation on it, it will be changed to 1111111111111111, i.e. True, but this is the binary representation of the signed integer -1.
A bit of 1 at the most significant position signals a negative number for signed numbers. Changing the sign of a number happens by inverting all the bits and adding 1. This is called the Two’s complement.
Let us change the sign of 1111111111111111. First invert; we get:
0000000000000000
Then add one:
0000000000000001, this is 1.
This is the proof that 1111111111111111 was the binary representation of -1.
UPDATE
Also, when comparing these values do not compare
x = -1
or
x = 1
instead, do compare
x <> 0
this always gives the correct result, independently of the convention used. Most implementations treat any value unequal zero as True.