Binary addition follows the same carry-over logic as decimal arithmetic, applied strictly to ones and zeros. This topic builds familiarity with binary number systems beyond simple conversion.
Adding Binary Numbers
We're going to learn how to add binary numbers together. If you had two binary numbers, how do you add those together? Quite honestly, this is not a skill that you're going to be using regularly, and I wouldn't say that this is mandatory for this course. However, I threw this in here because it adds more detail when dealing with these binary numbers. Let's figure out how to do this and get some practice at it, just to get more experience with working with these binary numbers.
I'm going to use this chart for my demo. You wouldn't necessarily need this chart to go through this process, but it's going to make it nice and easy and organized as I go through this.
What I'm going to do is add a 0 1 1 1 with a one zero zero one and see what that looks like. If I were to go through this process: one plus one can't equal 2, right, it's binary, so this column gets reset and we carry a 1 to the next column. One and one once again creates two, so we're going to reset that column and carry a 1 to the next column right there. If you notice, this is very similar to the decimal system, except that we're just using ones and zeros rather than zero through nine. So here again I'm going to have to reset this, carry a one, and then I'm going to have to do the same thing with this column, reset it and then carry a 1 to the next column. There are no numbers there, so I'll just add a 1 there. That is the answer; this is what we came up with.
One other scenario that I want to show you, though, is if you are carrying. Let's say we have one one one one one, and we'll do a zero one one one. This is going to be a little bit more unique when we do this, so let's take a look and see what the results are.
One and one, we're going to say, resets that and we carry a one, and now we have three. What do we do with that? Well, one of the ones can stay here, and the other two we can carry to the next column. The same thing happens here: one of the ones can stay, and the other two can carry a one to the next column. Now we've got two right there, so we'll reset that and carry a one over here, and so there's one. That is the answer right there.
So when you have more than — if you have like three, and it's an odd number, then one of the ones can remain there in the column while you carry over the other.
For this exercise, what you're going to do is add this column to this column. In this example right here, we've got one zero zero zero and we've got a zero one zero one. If I were to go through here: zero and one is one, zero and zero is zero, zero and one is one, and one. So the answer to this line is one one zero one. Go ahead and write all of this down, go through it, and see what answers you come up with, and then we'll check our work.
Once you've done that, this is the answer right here. Double check your work and make sure it's good.
Hopefully you did that well. Once again, this is not critical that you have this information down, but it's just another way to work with these binary numbers, and the more you can work with them, the better you'll understand them.
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