Why does ~2 equal -3 in Python?

Understanding Python's Bitwise Complement Operator (~ Tilde)

Introduction

The bitwise complement operator (~) is a powerful tool in Python that performs a bitwise operation on a numeric value. It's commonly used to invert the bits of a number, which can have interesting effects on the value's representation.

Why ~2 Equals -3

One of the intriguing aspects of the bitwise complement operator is its behavior when applied to the number 2. The result of ~2 is -3. To understand why this happens, we must examine the concept of two's complement.

Two's Complement

In computer systems, negative numbers are typically represented using the two's complement method. In two's complement, a negative value is obtained by inverting the bits of its positive counterpart and adding one.

For example,

• Positive 2: 0000 0010
• Invert bits: 1111 1101
• Add one: 1111 1110

Bitwise Complement ~2

When the bitwise complement operator is applied to 2, it simply inverts every bit in the binary representation of 2. The inverted bits, when interpreted in two's complement, represent -3.

Steps:

• Start with 2: 0000 0010
• Invert bits: 1111 1101
• This inverted value represents -3 in two's complement

Operator's Function

The primary function of the complement operator (~) is to flip bits. However, the interpretation of the resulting bit pattern is determined by the underlying machine or context within which the operator is being used.

Remember:

• ~ tilde complements (flips) bits.
• The meaning of the resulting bit pattern is determined by the machine or context.

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