Binary addition
Binary can be added together. Let's add 7 and 14 together as an example.
7
| Decimal | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|
| Binary | 0 | 0 | 1 | 1 | 1 |
14
| Decimal | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|
| Binary | 0 | 1 | 1 | 1 | 0 |
21
| Decimal | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|
| Binary | 1 | 0 | 1 | 0 | 1 |
The rules for addition are described below:
| 0+0 | 0 |
| 1+0 | 1 |
| 0+1 | 1 |
| 1+1 | 0 carry 1 |
| 1+1+1 | 1 carry 1 |
7 and 14 are 0111 and 1110. We add the first digits, this gives us 1, since 1 + 0 = 1.
| 0111 |
| 1110 |
| 1 |
Next, we add 1 and 1. This gives us 2, which in binary is 10. So we write down 0, and carry the 1.
| 1 |
|---|
| 0111 |
| 1110 |
| 01 |
Now, since we carried a bit, we have 3 bits to use. This gives us 3, which is represented as 11. So we write down 1 and carry the other 1.
| 1 |
|---|
| 0111 |
| 1110 |
| 101 |
Since we carried 1, we need to add 1 + 0 + 1, which equals 2. This in binary is 10, so we write that down.
| 0111 |
| 1110 |
| 10101 |
This seems pretty simple, but binary addition overflow can occur.