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:

• \( Num \) — Input number (-128 to 127)
• \( \sim \) — Bitwise NOT operation
• \( \& 0xFF \) — Masking to 8 bits

Explanation: The formula inverts all bits of the number (NOT operation), adds 1, and ensures the result is an 8-bit value.

3. Importance of 2's Complement

Details: 2's complement representation simplifies arithmetic operations in computers as addition and subtraction can be performed using the same hardware. It also eliminates the problem of negative zero found in other representations.

4. Using the Calculator

Tips: Enter any integer between -128 and 127. The calculator will show the 2's complement value along with its binary and hexadecimal representations.

5. Frequently Asked Questions (FAQ)

Q1: Why is 2's complement used?
A: It simplifies hardware design by allowing the same circuits to handle both addition and subtraction, and it provides a unique representation for zero.

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

Q3: How is overflow handled in 2's complement?
A: Overflow occurs when a result exceeds the representable range. In 8-bit arithmetic, results wrap around from 127 to -128 or vice versa.

Q4: What's the difference between 1's and 2's complement?
A: 1's complement simply inverts all bits, while 2's complement inverts and adds 1, eliminating the negative zero problem.

Q5: How is 2's complement converted back to decimal?
A: If the most significant bit is 1 (indicating negative), invert all bits, add 1, and add a negative sign to the result.