1. What is 2's Complement?

2's complement is a mathematical operation on binary numbers used to represent signed integers in computer systems. 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 formula:

Where:

• \( \sim\text{Number} \) — Bitwise NOT of the number
• \( + 1 \) — Add 1 to the result
• \( \& 0xFF \) — Mask to 8 bits

Explanation: The operation inverts all bits of the number and adds 1, then masks to 8 bits to ensure the result fits within 8-bit representation.

3. Importance of 2's Complement

Details: 2's complement representation allows for efficient arithmetic operations on signed integers and eliminates the problem of negative zero that exists in other signed number representations.

4. Using the Calculator

Tips: Enter an 8-bit integer between -128 and 127. The calculator will compute and display the 2's complement in decimal, binary, and hexadecimal formats.

5. Frequently Asked Questions (FAQ)

Q1: Why is 2's complement used in computers?
A: 2's complement allows for simple hardware implementation of arithmetic operations and eliminates the need for separate subtraction circuitry.

Q2: What is the range of 8-bit 2's complement numbers?
A: The range is from -128 to 127, where the most significant bit indicates the sign (1 for negative, 0 for positive).

Q3: How do you convert back from 2's complement?
A: To get the original number from its 2's complement, simply apply the same operation: take the 2's complement of the 2's complement.

Q4: What happens if I input a number outside the 8-bit range?
A: The calculator only accepts numbers between -128 and 127. Values outside this range are not valid 8-bit integers.

Q5: Can this calculator handle floating-point numbers?
A: No, this calculator is specifically designed for 8-bit integer 2's complement conversion.