1. What is 2's Complement Addition?

2's complement is a mathematical operation on binary numbers that is commonly used in computing to represent signed integers. Addition in 2's complement follows the same rules as regular binary addition.

2. How Does the Calculator Work?

The calculator performs 2's complement addition using the following steps:

Where:

• \( A \) — First binary number in 2's complement
• \( B \) — Second binary number in 2's complement
• \( Add \) — Result of the addition in binary

Explanation: The calculator treats the inputs as 2's complement numbers, performs binary addition, and returns the result in binary format.

3. Importance of 2's Complement

Details: 2's complement is crucial in computer systems for representing signed numbers and performing arithmetic operations. It simplifies hardware design by using the same circuits for addition and subtraction.

4. Using the Calculator

Tips: Enter two binary numbers (consisting of 0s and 1s) in the input fields. The calculator will display their sum in binary format.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of numbers this calculator can handle?
A: The calculator can handle any binary numbers that fit within PHP's integer limits (typically 32-bit or 64-bit depending on your system).

Q2: How does overflow work in 2's complement addition?
A: In 2's complement, overflow occurs when the result exceeds the representable range. The calculator doesn't currently detect or handle overflow.

Q3: Can I enter numbers in other formats (hex, decimal)?
A: Currently, the calculator only accepts binary inputs (0s and 1s).

Q4: What happens if I enter invalid binary numbers?
A: The calculator will only accept strings containing 0s and 1s. Other characters will be rejected.

Q5: Why use 2's complement instead of other representations?
A: 2's complement has several advantages including a single representation for zero and simpler arithmetic operations.