Why Does `~2` Yield `-3` in Python?

Understanding Python's Bitwise Complement Operator (~)

Why does ~2 yield -3 in Python? The bitwise complement operator (~), often denoted as a tilde, plays a crucial role in bitwise operations. To grasp its workings, let's delve into the concept of two's complement representation.

Negative integers in Python are stored using two's complement, which involves inverting the binary representation of the positive counterpart and adding one. For instance, the binary representation of -2 in two's complement is:

1111 1110

This is obtained by inverting the bits of two's binary representation (0000 0010) and adding one. The leading bit serves as the sign bit, signifying a negative value.

Now, let's examine how applying the complement operator to two leads to -3:

two: 0000 0010
~two: 1111 1101

We simply invert the bits of two, resulting in the inverted representation. However, this inverted representation happens to align with the two's complement representation of -3, which is:

1111 1101

Therefore, applying the complement operator to two effectively provides the two's complement representation of -3.

It's important to note that the complement operator (~) merely flips the bits of a number. The actual interpretation of these bits depends on the machine architecture and context in which they are used. In the case of integers in Python, the machine interprets the inverted bits according to the two's complement representation for negative numbers.

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