Binary Addition Calculator
Add two binary numbers together and see every carry bit along the way. This calculator shows the full binary sum plus the decimal equivalents so you can verify your work instantly.
Binary addition follows the same column-by-column approach you already know from decimal addition, but with only two digits: 0 and 1.
Binary Addition Rules:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (write 0, carry 1)
- 1 + 1 + 1 = 11 (write 1, carry 1)
How It Works:
Start from the rightmost bit and work left, just like decimal addition. When a column adds up to 2 or 3, you write the remainder and carry a 1 to the next column.
Example:
Adding 1011 (decimal 11) and 1101 (decimal 13):
| Carry | 1 | 1 | 1 | 0 | |
|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | ||
| + | 1 | 1 | 0 | 1 | |
| = | 1 | 1 | 0 | 0 | 0 |
Result: 11000 (decimal 24). That checks out since 11 + 13 = 24.
Binary addition is the foundation of how every computer processor handles arithmetic. ALUs (arithmetic logic units) use chains of full adders to process numbers bit by bit.