Binary Addition
Binary addition works like decimal addition, column by column from the right, with one difference: 1 + 1 makes 10, so you write 0 and carry 1. That rule and three simpler ones are all you need.
Updated
The rules of binary addition
| Sum | Result | Write | Carry |
|---|---|---|---|
| 0 + 0 | 0 | 0 | 0 |
| 0 + 1 | 1 | 1 | 0 |
| 1 + 0 | 1 | 1 | 0 |
| 1 + 1 | 10 | 0 | 1 |
| 1 + 1 + 1 | 11 | 1 | 1 |
Worked example: 1011 + 0110
Line the numbers up on the right and add one column at a time.
- 01
Column 1 (right)
1 + 0 = 1. Write 1, nothing to carry.
- 02
Column 2
1 + 1 = 10. Write 0, carry 1.
- 03
Column 3
0 + 1, plus the carried 1, is 10. Write 0, carry 1.
- 04
Column 4
1 + 0, plus the carried 1, is 10. Write 0, carry 1.
- 05
The last carry
Write the carry on the left. The answer is
10001, which is 17: 11 + 6.
Try it: add two binary numbers
Type two numbers to see the carries over each column. The binary calculator also subtracts, multiplies and divides.
Binary calculator
Binary
Practice: 10 problems
Type each answer in binary. Leading zeros don't matter.
Checking your answer
Convert both numbers and the answer to decimal: if the decimals add up, so does the binary. 1011 + 0110 = 10001 checks out because 11 + 6 = 17. The binary to decimal converter does the conversion for you.
Frequently asked questions
What are the rules of binary addition?
0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10, which means write 0 and carry 1. When a carry comes in as well, 1 + 1 + 1 = 11: write 1 and carry 1.
What is 1 + 1 in binary?
10, which is two: a 1 in the twos place and a 0 in the ones place. It is not ten.
What is 1 + 1 + 1 in binary?
11, which is three: a 1 in the twos place and a 1 in the ones place. In a column sum, write 1 and carry 1.