Lesson video

Hi, I'm Rebecca, your computing teacher for the Data Representations unit.

Now for this lesson, you're going to need a pen and paper so that you can do your calculations and make any notes.

You're also going to need to make sure that you have removed as many distractions as you possibly can out of the way so you can really focus.

Once you've done all of that, we can begin.

In this lesson, you will recap conversions between number bases and you'll perform addition of three binary numbers.

Let's do a quick quiz then to get started, here we go.

What is the number base of the decimal number system? Which one is it? Take a look.

It is 10, well done.

What is the number base of the hexadecimal number system? It's got 16 digits, so it must be 16.

What is the number base of the binary system? Have a think about that well.

It is number two.

Well done.

What is the name of the tiny switches inside a computer? Can you remember that one? That was few lessons ago now that one, what was that name? It was the transistor.

Which of these is equivalent to one byte of storage and it says select all, so select all that apply there.

So then there's going to be more than one, so take a good look.

See which one's equivalent to one byte.

It was those three, did you get all three? Here's the next one, so what is F? And it's got a base of 16, so it must be a hex value in decimal.

Can you work that out? It is 15, well done.

Now here we go, What is D? Again, base 16, so it's a hex value in binary this time.

So you probably have to convert it to decimal first and then converted to binary, maybe.

Here we go.

It was one, one, zero, one.

Now we're going to have a look at some addition.

Let's just have a quick reminder of how it works first.

So we've got those rules there in the bottom left-hand corner for you to take a look at and then if we've got a number like one, one, zero, add one, zero, one, then we use column addition.

We work from right to left and we use those rules for each one.

So you've got what? A zero plus one is one if we look at the rules, we just take a one there and then one with a zero is one, so we're just following those rules again and then we've got one add one, makes one, one.

So because there's nothing else on the left-hand side, now we can just put one, zero there.

So one, one, zero plus one, zero, one is one zero, one, one in binary and we can double check that by doing six, add five because that's the two binary numbers that we're adding together and the answer is 11 and we can compare that to a binary answer, which is also 11 because eight plus two plus one is 11.

So we know we've got the answer right and it's always important to check it as well, especially, when you're in those little stressful conditions, you might make a little mistake with a one or a zero somewhere along the way.

It's just always best to double check what you're working at.

So I want you to try it yourself now, so pause the video.

You might want to draw that column addition table as well as help you out.

And I want you to pause the video while you answer those five questions, off you go.

Great, so here's the answers slide.

So the first one A, the answer was one, one, one.

For B, the answer was one, one, zero, one.

For C, the answer was one, zero, zero, zero, one.

For D, it was one, one, one, zero.

For E, it was one, zero, one, zero, zero.

Brilliant.

Now let's try some Shifting.

Let's see what you can remember about that.

So which direction do you Shift to multiply? Which direction is it? You Shift Left because the numbers increase, don't they? You Shift Left.

How many Left Shifts would you make to multiply by eight? So you've got that clue there with the table where you've got one, two, four, eight, how many Shifts do you make to get to that number eight? You make three Shifts.

So which direction do you Shift to divide? Pretty obvious now, I hope.

It's Right.

How many Right Shifts would you make to divide by four? It was two, okay.

So true or false, any remainders from division will be discarded.

Can you remember that one? It is true, well done.

So some binary Shifting that I want you to try yourself then now.

So take a look at these, pause the video while you do that, I've drawn that table there to help you so you can keep that on your screen or you can draw it yourself in your book as well, that'd be a good idea or on your paper.

So pause the video while you think about that.

Fantastic, so here's the answers slide.

So the first one for multiply for A was one, one, one, one, zero, zero, zero.

For B, it was one, zero, one, one, zero.

For C, it was one, one, one, one, zero, one, zero, zero.

And then for the divide one, A was zero, zero, one, zero, B was zero, zero, zero, one, one, one, zero.

For C, it was zero, zero, one, one, one, zero.

Brilliant, so let's take a look at the rest of it then.

So what we're going to do now is we're going to just take a look at adding three binary numbers together and when you look at this, you might think, "Gosh, this is really, really tricky," but actually if we follow those rules, like we've been doing with just two numbers added together, then hopefully, it's not going to be as tricky as you might think it is.

So let's take a look.

So with binary addition when it's three numbers, we just do exactly the same thing.

We put it into columns, we start from right to left and we follow those rules all the way across.

So the first one then, we've got zero add one, add one, so basically, we're doing one add one, which is one zero.

We put the one down below because it's going to be moving to the next column and we put a zero in that column.

We then look at the next one, so you've got zero, add one, add zero, add one this time, which is essentially one add one, so it's just one, zero again.

So we place it in the next column, underneath the one and then the zero in the current column and we discard the other one, we can just cross it out because we've dealt with that one now, then we look at this column, one add one, add one, so we look for our rows again.

So one add one, add one, is one, one and we've still got a bit more left.

So we put it down at the bottom and the other one in the current column and then we're just left with our last number and our last rule, one add one is one, zero.

And because we've got nothing left, we can just put one, zero there.

So you can see, it might look complicated at the beginning, but as long as we're still following those rules again, we should be okay.

So one, zero, zero, zero plus one, one, one plus 101 is 10,0100 in binary, which is eight plus seven plus five and if we do that in decimal and the answer is 20, and then we can just double check that we've got 20 there with our answer.

So if we look there, we have got one, two, four is selected so four plus eight was 16, four plus 16 is 20 so we've definitely got that right and it's always very important to double check, okay.

So try it yourself.

Use that column addition again, use that table to help you if you want to draw it out in that layout, use the rules too, pause the video while you have a go at those values.

Fantastic then, so let's look at the answers.

So A was one, zero, one, one, zero, B was one, zero, one, zero, zero, C was one, one, one, zero, D was also one, one, one, zero and E was one, one, zero, zero, zero.

Fantastic, so that was a recap of everything that we've done in all of those lessons so far and hopefully, let's just do your thumbs up, your thumbs down.

Hopefully you were sort of on the closer bit to a thumb up there, and you're really starting to get it now and if you didn't, this is a really, really important time to just go back over those lessons, those lessons aren't going anywhere.

So if you struggled with maybe the addition or with the hex conversions, just go back to that lesson and do that lesson again and just keep practising over and over again 'cause you will get it eventually.

You might find it easy when I'm talking you through it, but not be able to remember it when you're on your own doing it independently.

It literary just takes practise, So the more and more you do, the more practise you have, the more likely it's going to just stick in your mind, how to actually do it.

So don't feel bad about going back on those other lessons.

It's completely natural for people to do that.

So just do it if you need to, but if you aced it, then you're ready to move on to the next lesson.

See you soon.