1. What is Binary Addition?

Binary addition is the fundamental operation in binary arithmetic, similar to decimal addition but using base 2. It follows the same principles but with only two possible digits (0 and 1) and specific rules for carrying over.

2. How Does Binary Addition Work?

Binary addition follows these basic rules:

For multiple-bit numbers, addition proceeds from right to left, with carries propagating to the left.

3. Step-by-Step Calculation

Example: Adding 101 (5 in decimal) and 110 (6 in decimal)

• Step 1: Add rightmost bits (1 + 0 = 1)
• Step 2: Add middle bits (0 + 1 = 1)
• Step 3: Add leftmost bits (1 + 1 = 0 with carry 1)
• Final result: 1011 (11 in decimal)

4. Using the Calculator

Instructions: Enter two binary numbers (containing only 0s and 1s) and click Calculate. The calculator will show their binary sum.

5. Frequently Asked Questions (FAQ)

Q1: What happens if numbers have different lengths?
A: The calculator automatically pads the shorter number with leading zeros before addition.

Q2: How is overflow handled?
A: Any final carry becomes the most significant bit of the result.

Q3: Can I add more than two numbers?
A: This calculator adds two numbers at a time. For multiple numbers, add them sequentially.

Q4: What's the maximum number of bits supported?
A: The calculator can handle very long binary numbers, limited only by PHP's string length capabilities.

Q5: How does this relate to computer arithmetic?
A: Binary addition is the foundation of all arithmetic operations in digital computers and processors.