Adding & Subtracting in Binary

Adding in binary is the same column method you use in decimal. Work right to left, and carry when a column overflows. The only difference: a binary column overflows the moment it passes 1.

The four single-bit sums are the whole of it:

The last row is the key one: $1 + 1 = 2$, which is $10$ in binary, so the column writes 0 and carries 1.