Binary addition and overflow

Adding in binary

Every time your phone adds two numbers, it does it in binary. At school you add fifty-eight and sixty-seven column by column, carrying a one. A computer uses exactly the same method. The only difference is that it has just two digits, zero and one.

Why one plus one is ten

Here is the one idea that makes binary addition work. In binary, the columns are one, two, four, eight. So the number two is written one, zero: one lot of two, and no ones. That is why one plus one in binary is one, zero. We write zero and carry one, just like nine plus one in denary.

The four rules

So there are only four rules. Zero plus zero is zero. Zero plus one is one. One plus one is zero, carry one. And when a carry arrives in a column that already has two ones, there are three ones: write one, carry one.

A small one first

Let us start small, with four bits: 0 1 0 1 plus 0011. Always start from the right. One plus one is zero, carry one. Then zero plus one plus the carry: zero, carry one. Then one plus zero plus the carry: zero, carry one. And the last column, zero plus zero plus the carry, is one. The answer is 1000.

Always check in denary

Here is a habit that saves marks. Turn both numbers into denary: 0 1 0 1 is five, and 0 0 1 1 is three. Five plus three is eight, and 1 0 0 0 is eight. The binary answer is right.