1. What is 2's Complement?

Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation. It's the most common method of representing signed integers in computers.

2. How Does the Calculator Work?

The calculator uses the 2's complement conversion formula:

Where:

• Hexadecimal value is converted to binary
• If most significant bit is 1, the number is negative
• For negative numbers: invert all bits, add 1, then apply negative sign
• For positive numbers: convert directly to decimal

Explanation: The 2's complement system allows for efficient representation of both positive and negative numbers in binary form.

3. Importance of 2's Complement

Details: 2's complement is crucial in computer systems for arithmetic operations, as it simplifies the hardware design for addition and subtraction of signed numbers.

4. Using the Calculator

Tips: Enter a valid hexadecimal value and select the bit length (8, 16, or 32 bits). The calculator will determine if the value represents a positive or negative number in 2's complement form.

5. Frequently Asked Questions (FAQ)

Q1: Why is 2's complement used?
A: It simplifies arithmetic operations in computers, as addition and subtraction can be performed with the same hardware regardless of sign.

Q2: What is the range for 8-bit 2's complement?
A: -128 to 127 (80 to 7F in hex for positive, 80 to FF for negative).

Q3: How do I recognize a negative number?
A: In 2's complement, if the most significant bit is 1, the number is negative.

Q4: What happens if I enter a value too large?
A: The calculator will show an error if the hexadecimal value exceeds the selected bit length.

Q5: Can I convert decimal back to hex 2's complement?
A: This calculator is one-way (hex to decimal), but the reverse conversion is possible by applying the 2's complement rules in reverse.