1. What is 2's Complement?

The 2's complement is a mathematical operation on binary numbers used in computing to represent signed integers. It's the most common method of representing signed numbers in computers.

2. How Does the Calculator Work?

The calculator uses the 2's complement formula:

Where:

• \( \sim\text{Hex} \) — Bitwise NOT of the hexadecimal input
• \( + 1 \) — Add one to the result

Explanation: The calculator first converts the hex input to binary, performs bitwise NOT operation, adds 1, and converts the result back to hexadecimal.

3. Importance of 2's Complement

Details: 2's complement representation allows for efficient arithmetic operations in computers and simplifies hardware design for signed number operations.

4. Using the Calculator

Tips: Enter a valid hexadecimal number (0-9, A-F). The calculator will automatically determine the appropriate bit length (8, 16, 32, or 64 bits) for the calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is 2's complement used?
A: It simplifies arithmetic operations (addition/subtraction can use the same hardware) and eliminates the problem of negative zero.

Q2: What's the range for an 8-bit 2's complement number?
A: -128 to 127 (0x80 to 0x7F in hexadecimal).

Q3: How do I know if a hex number is negative in 2's complement?
A: If the most significant bit is 1 (for 8-bit: if first hex digit is 8-F; for 16-bit: if first hex digit is 8-F, etc.).

Q4: Can I convert back from 2's complement?
A: Yes, applying the same operation (invert bits and add 1) will return the original positive number.

Q5: Does this work for any bit length?
A: Yes, the calculator automatically handles 8, 16, 32, or 64 bit numbers based on input size.