1. What is Bitwise Inversion?

Bitwise inversion (also known as bitwise NOT) is a unary operation that performs logical negation on each bit of a number, flipping 0s to 1s and 1s to 0s in the binary representation of the number.

2. How Does the Calculator Work?

The calculator performs the bitwise NOT operation:

Where:

• \( \sim \) — Bitwise NOT operator
• \( x \) — Input integer

Explanation: The operation flips all bits in the binary representation of the number, which mathematically results in the negative of the original number minus one.

3. Importance of Bitwise Operations

Details: Bitwise operations are fundamental in low-level programming, cryptography, and hardware manipulation. They are used for efficient data packing, flag manipulation, and performance-critical applications.

4. Using the Calculator

Tips: Enter any integer value (positive or negative) to see its bitwise inversion. The calculator works with 32-bit signed integers (range: -2,147,483,648 to 2,147,483,647).

5. Frequently Asked Questions (FAQ)

Q1: Why does bitwise inversion result in negative numbers?
A: In two's complement representation (used by most computers), the bitwise NOT of a positive number gives its negative counterpart minus one.

Q2: What's the difference between logical NOT and bitwise NOT?
A: Logical NOT (!) returns a boolean (true/false), while bitwise NOT (~) operates on all bits of a number.

Q3: How does this work with negative numbers?
A: The operation is symmetric - inverting a negative number gives its positive counterpart minus one.

Q4: What's the practical use of bitwise inversion?
A: Common uses include creating masks, toggling bits, and implementing efficient arithmetic operations.

Q5: Does this work differently in different programming languages?
A: The basic operation is consistent, but behavior with unsigned integers or numbers beyond 32 bits may vary by language.