In the last unit, we saw how to represent numbers in computers using binary bits,

but now we can represent numbers, that's an important thing.

Now the whole point of representing something is if we want to manipulate it.

What kind of manipulations do we want to do with bi, with numbers?

Well we want to add them, subtract them, multiply them and so on.

This is what we're going to learn how to do in this unit.

Well, not all of them.

What we will really be talking about is how to add.

Once we do that we'll basically get the whole rest of the other operations

almost for free.

It turns out that once we understand how to represent negative numbers,

which we will do in next unit, we will be able to get subtraction for free and

to understand which of two numbers is greater for free.

Multiplication and divisions are more complicated, but nicely enough,

we can actually postpone them to software.

We will not build in hardware any multiplication or division eh, circuitry.

But rather, we will actually let software do it and

things are much easier to do in software because you just have to

write little programs rather than actually connect stupid little devices.

So we get two sequences of binary numbers.

How can we add them?

Well one way we already know how to do, and that's going to be very easy.

We convert them to decimal.

We add the decimal numbers.

That we know how to do from second grade.

We get a decimal number.

We convert it back to binary.

That we just learned how to do.

And we get the answer.

This is great and fine, but of course that's not what a computer does.

A computer doesn't know how to add decimal numbers

without first converting them to binary numbers.

So we need to figure out how to actually do the addition of binary numbers, and

directly, without converting them to decimal.