what is the purpose of ~ symbol in python?

Question

Input = ~7 Output = -8 Here I can understand that 1's complement of 7 is -8

Input = ~6 Output = -7 But here 1's complement of 6 isn't -7 instead it is -9

Correct me if I am wrong

`But here 1's complement of 6 isn't -7 instead it is -9` Why would it be -9? — tkausl, Mar 21 '21 at 17:58
Does this answer your question? [Why the binary representation is different from python compiler than what we know on paper?](https://stackoverflow.com/questions/62332193/why-the-binary-representation-is-different-from-python-compiler-than-what-we-kno) — MisterMiyagi, Mar 21 '21 at 18:04
Does this answer your question? [Confusion with 1's compliment binary representation](https://stackoverflow.com/questions/63886277/confusion-with-1s-compliment-binary-representation/63887080) — MisterMiyagi, Mar 21 '21 at 18:10

score 2 · Answer 1 · answered Mar 21 '21 at 18:02

~ is the bitwise operator:

It takes one bit operand and returns its complement. If the operand is 1, it returns 0, and if it is 0, it returns 1

In [84]: bin(6)
Out[84]: '0b110'

In [85]: bin(-7) # 2's complement of `6`
Out[85]: '-0b111'

So, ~6 = -7 is correct.

score 0 · Answer 2 · answered Mar 21 '21 at 18:05

https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations

The unary ~ (invert) operator yields the bitwise inversion of its integer argument. The bitwise inversion of x is defined as -(x+1). It only applies to integral numbers.

So ~6 = -7 as per the definition of the ~ operator.

score 0 · Answer 3 · answered Mar 21 '21 at 18:17

0

~ is a (NOT) Bitwise Operator which simply means that:
if a = 60 in binary a = 0011 1100
so ~a = - 61 in binary a = 1100 0011
Did you noticed how the binary code just inverted?!

answered Mar 21 '21 at 18:17

Waleed Elshatlawy

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1

You can check that in your python editor... it's ~60 = - 61 – Waleed Elshatlawy Mar 22 '21 at 19:41
Sorry about that - I just misread your answer. – Adrian Mole Mar 22 '21 at 19:45

score 0 · Answer 4 · answered Mar 21 '21 at 18:28

The tilde symbol means to flip all the bits in a number, zeros go to ones, and ones go to zeros. In python this is tricky, because integers in python are dynamic in size, and grow as the number grows. The number 6 is 3 bits long, the number 10 is 4 bits long, etc.

In another language like C, an int has a specific length, like int32 are integers that take up 32 bits, hence the tilde symbol makes more sense. And flips the 32 bits altogether. (Note that in memory, the highest bit typically represents the sign of the integer).

Due to the dynamic size of python integers, the tilde symbol requires knowing the bit length first. If the integer is positive, then we need to subtract the higher bit to represent switching the sign at that bit length. For a int5 number, this would look like

~10 = ~0b1010 = 0b0101 - 0b10000 = 0b10101 = -11

If the integer is already negative, then we need to add an extra bit and flip that directly.

~(-11) = ~-0b0101 = ~0b10101 = 0b01010 = 0b1010 = 10

Unfortunately, python interprets 0b10101 as an uint5 integer without a sign bit (a int6 integer). Hence, these statements are only equal on paper, not as python code.

what is the purpose of ~ symbol in python?

4 Answers4