Binary addition

We add binary values in columns just like we would with denary addition.
Each column is classified on the basis of place-value. In denary this is 10, in binary it is 2.
When we conduct a binary addition, we add the binary values as if they were normal integers but we represent the sums as binary.
- For example: $1 + 1 = 2$ for the calculation but the sum is $10$

Examples

Example one

$$ 1010 + 0111 = 10001 $$

$$ 10 + 7 = 17 $$

In the first column: $1 + 0 = 1$, so we simply put the binary value for $1$:

1010
0111
____
   1

In the second column: $1 + 1 = 2$. In binary this is represented as $10$. So we put $0$ beneath the bar and carry the $1$:

In the third column, we repeat the previous process. We are presented with $1 + 0 + 1$ which is $2$. As $2$ is $10$ in binary, we put the zero beneath the line and carry the $1$:

In the final column, we again have $1+1$ giving us $2$ or $10$ but at this point we cannot carry any more because we have reached the final column. So instead of carrying the $1$ we just put both digits beneath the line $10$.

Example two

$$ 1001 + 0111 = 10000 $$

$$ 9 + 7 = 16 $$