Addition is a vital skill when adding binary numbers. Addition forms the base of all mathematics operations in computer systems. Therefore it is vital to learn how to add binary numbers together. The good news is that if you know how to add decimal numbers together then binary addition should be a breeze.
There are a few rules to remember when learning to add binary. As we only have two digits we can summarise this into four rules:
You can try this in the above binary addition calculator to confirm these rules are correct.
The best way to learn how to complete binary addition is through some worked examples. Follow along with our two worked examples below.
In the below example we add 2 (10) and 5 (101) together in binary. This is an easy example as it does not include any carries.
In the below example we add 7 (111) and 23 (10111) together in binary. This is a harder example as it includes having to use carries.
Using our free binary addition calculator is easy. First type the first number you want added in the first input box. This will have to be in binary (so use 1s and 0s only) but the calculator will show you the converted decimal version next to the input so you can check your work. Next input the second number (the one you want added) into the second input box. Again this will have to be in binary but the calculator will convert this for you to decimal so you can check. Finally click calculate to get your result. Both the binary and decimal result will be provided. If you want to calculate more combinations, you can reset the calculator at the top left of the tool.
| A | B | A + B | Carry |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 10 | 0 | 10 | 0 |
| 10 | 1 | 11 | 0 |
| 11 | 0 | 11 | 0 |
| 11 | 1 | 100 | 1 |
| 100 | 0 | 100 | 0 |
| 100 | 1 | 101 | 0 |
| 101 | 0 | 101 | 0 |
| 101 | 1 | 110 | 0 |
| 110 | 0 | 110 | 0 |
| 110 | 1 | 111 | 0 |
| 111 | 0 | 111 | 0 |
| 111 | 1 | 1000 | 1 |
Like all tools on binarytables.com the above calculator is free to use!