Likely the first way you’d have learnt addition would have been column addition for any non-single digit numbers. For example if we wanted to add 105 and 27 we’d end up with a table that looked something like this.
| Hundred’s | Ten’s | Unit’s | |
|---|---|---|---|
| 105 | 1 | 0 | 5 |
| +27 | 21 | 7 | |
| =132 | 1 | 3 | 2 |
Where as in binary we only have 2 options.
| 128’s | 64’s | 32’s | 16’s | 8’s | 4’s | 2’s | 1’s | |
|---|---|---|---|---|---|---|---|---|
| 105 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| +27 | 01 | 01 | 01 | 11 | 1 | 01 | 11 | 1 |
| =132 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
As you can see the ripple of carrying the 1 up moves a lot further in binary than it does in decimal. Now try 97 + 155:
| 256’s | 128’s | 64’s | 32’s | 16’s | 8’s | 4’s | 2’s | 1’s | |
|---|---|---|---|---|---|---|---|---|---|
| 97 | |||||||||
| +155 | |||||||||
| Carry | |||||||||
| = |