Binary Addition
Computers add binary all the time and it is really simple to do, they are only adding 1's and 0's after all. Watch the video first, this is much, much easier to follow with a talked through worked example.
There are four rules you need
- 0 + 0 = 0
- 1 + 0 = 1
- 1 + 1 = 10
- 1 + 1 + 1 = 11
Let's look at an example to see how it works in practice:
Note: When we add 1 + 1 in binary we get 10.
We write in the 0 in the column we are adding, and carry the 1 (to the next column to the left)
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | |
| + | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 |
= | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| carried | 1 | 1 | 1 | |||||
| sum done | 0+0+1 | 1+0+1 | 1+0+1 | 1+1 which = 10, | 1+0 | 1+0 | 1+0 | 1+0 |
Overflow error
As we only have 8 numerals in our standard binary numbers (8bit binary) , there comes a point where we have 1+1 in that 8th colum (the 128 one). we know it adds up to 10 but we have nowhere to carry the one over to. We need another column but it doesn't exsit. Our options are either to extend the columns past 8 which leads us to 16bit binary or we just drop the one and the answer becomes incorrect. This is called an Overflow error.