Lesson video

Hi, I'm Rebecca, your computing teacher, for the data representations unit.

For this lesson, you're going to need a pen and paper to answer any of the questions that I give you and to draw that table, that binary table that you're going to need.

You're also going to need to remove as many distractions as you possibly can so that you can really focus this lesson.

Once you've got that ready, we can begin.

In this lesson, you will recap binary to decimal conversions.

You'll count in binary.

You'll perform addition in binary and you'll perform binary shifts.

So let's get started.

You need to draw this table.

So draw this table now so that you can do the rest of the activities.

So we're going to convert these numbers from binary to decimal.

We're going to do it as quick fire as you can, but remember, you can always pause if I am going a little bit too fast.

So off we go.

One, one, one, what is that in decimal? It is seven.

So you've got four add two add one is seven.

So one, one, zero, one.

What's that in decimal? It is 13.

Let's look at the next one.

One, zero, one, one, zero.

I'll give you a little bit longer this time.

It's 22.

So one, one, one, zero.

What's that going to be? 11, 12, 13 or 14? It's 14.

Oh, here's a long one.

One, zero, zero, zero, zero, zero, one, one.

What's that going to be? It's 131.

Wow, that was a big long one.

So we're going to have a look now, see if you can remember about you converting from decimal this time to binary, so remember you've got to find the highest one that would fit into that value.

Then you've got to subtract it from the original value and move along from left to right through the table.

So pause the video while you have a go at that.

And here are your solutions.

So pause the video again so that you can self-mark your answers.

We're now going to look at counting in binary.

Before you can perform addition in binary, you need to learn to count in binary.

Let's take a look at how we count in decimal first.

So this is something you probably learned a long time ago, but you've never really thought about it in that much detail, but this is how it works for the decimal numbers.

Say, start with zero, one, two, three, four, five, six, seven, eight, nine, and you get to nine and you run out of those decimal digits that we've got.

So there are no digits left to use in the number system.

So we move to the next column.

So the one goes into the next column and a zero goes into the other column.

And then you start counting again.

Now we work our way through all of the digits again, like so, and we run out of digits again.

So we have to move to the other column.

And now that two is now worth two times 10.

So we just need the zero in that ones column.

And so it continues.

But in binary it works out in exactly the same way.

We just have less digits, which is just a one and a zero, but we do the same thing.

It will go much faster though.

So you've got a zero, one, we run out of digits, so we move to the next column, which now has a one in it, but we have a zero in the original one.

And then one again, run out of digits.

So we have to put a one in the next column and you've got zeros in the other columns.

And then we count again, like so, and then we run out of digits again.

So we have to go to the next column.

We move up the columns much, much faster, don't we, because we only have two digits instead of 10.

So there we only counted to actually the number eight.

We moved up those columns really, really quickly.

That would have still been in that first one's column if we were looking at decimal numbers.

So let's count in binary.

So take a look at this.

You've got zero and you can see down the bottom there, we've got the base 10.

So that's going to be the decimal number so that you can see the equivalent and see if you can count it.

See if you can guess what the next value is while we're doing it.

So zero, one, one, zero, one, one.

What's next? One, zero, zero.

What's next? One, zero, one.

One, one, zero.

Then one, one, one.

Sometimes people get that a little bit confused, but I suppose with practise then that'll come to you a little bit better.

So we run out of digits.

so we go one, zero, zero, zero.

One, zero, zero, one.

And then one, zero, one, zero is our 10 in decimal.

Now there are four golden rules of binary addition.

So hopefully you've counted now.

You've started to see how those numbers go up.

And then these rules kind of apply to how we can count a little bit.

So rule one, zero plus zero is zero.

Now, hopefully that one's quite obvious to you 'cause that's exactly the same in decimal as well.

Zero add zero is zero.

And on the right hand side there, you can see I've started to put it in column addition as well.

So you can have a look at that, too.

So in decimal, zero add zero add zero.

So zero adds zero equals zero.

It's exactly the same.

Rule two, zero add one equals one.

Again, in decimal, it's exactly the same thing, isn't it? Zero add one is one.

Now this is where your head starts to go, huh, really? 'Cause actually rule three is one add one is one, zero.

You're like, is that 10? Is that, what is that? What actually is that, like? It's one, zero, 'cause it's in binary.

But actually in decimal, one add one is two, isn't it? One, zero in binary is also two.

It's just that in binary, it's one, zero.

Then you've got that fourth rule.

Which is one add one add one is one, one.

So again, little bit of a head scratcher there.

'Cause it looks like the number 11.

It's not the number 11, it's one, one.

So if you think about this in decimal terms, one add one add one is three in decimal terms, and in binary, one, one actually is three, isn't it? So if you remember those headings, you've got a one above the one on the right and you've got a two above the next one and that makes three.

So it does make sense, but it takes a little while to sort of get your head round these four rules and how they actually work.

And don't worry if you need to take this slow, you can always pause and come back and look at it if I am going a little bit too fast for you.

So I've put those rules in the bottom left hand corner so that you can keep referring to them.

Those rules are really, really important.

They'll seem not so important at the beginning, but the harder and harder these add addition get, so if you wanted to practise doing some eight-bit binary numbers and adding those together, then you probably definitely want those rules nearby to help you.

So it's definitely important to keep those there.

Even write them down now, if you want to, just so that you've got them for later, if you need them.

So we're going to do this one, binary addition.

So you've got one, zero, zero, add one, zero.

So first of all, we go back to those rules and we start, just like we would if we were adding two numbers in the decimal system.

We've got our column addition and we go for the right column first.

So zero add zero is zero.

So we just look at that rule and that's what we replicate there in that right hand column.

We then look at the next one.

So zero add one, so look at the rule.

Zero add one is one.

So we just put a one there.

And then again, we've got zero add one again, because there's nothing there in that second line there.

So we're just adding zero or adding nothing.

So we just put a one there.

So then you've got, one, zero, zero, add one zero is one, one, zero, and that's the answer.

And then we can just double-check it in binary.

So I always say it's a good idea to double-check your answers.

So if we look, one, zero, zero is actually four in decimal and one, zero is two in decimal.

Four add two is six.

Okay.

So then we can look one, one, zero.

Is that also six? Yes, it is.

So that's going to help us practise it.

So let's have a look at this next one then.

One, zero, zero, add one, zero, one.

So let's look at those rules again.

Zero add one is one.

Zero add zero is zero.

Now one add one, this is where it gets a little bit tricky 'cause we have to move to the next column.

Now there was nothing there in that column.

So we can just happily put that one there like that.

And the answer is one, zero, zero, one.

So one, zero, zero plus one, zero, one is one, zero, zero, one in binary.

And then we can do our double-check.

So four add five is nine in decimals.

So we've got a four.

Then we've got a five.

We add that together, it makes nine.

And then we can look at the sum at the bottom.

That makes nine as well, because that first one is in the one column.

And then the one on the left is in the eight column.

Eight plus one is nine.

So we can just double-check that we were right.

Let's try another one then.

One, oh, one plus one, one.

So let's look at these rules this time.

This is where these rules start to become really, really helpful.

So we've got there, one add one.

Now, if you look at our rules, one add one is one, zero, but we've also got something in the column to the left this time.

So we can actually put it underneath, or I don't know how you learnt your maths, but I always learned to put it underneath there because we want to move that one over into the two column.

But we want to also make sure that we count the other things that are in that two column.

So we move it below there.

So one add one is one, zero.

So we put the one down the bottom and the zero in that column where it should be.

Then we move on to the next one.

So now we've got zero add one, add one.

So we need to try and work that out.

Now we can ignore the zero, can't we, just look at that one add one.

So where's our rule for one add one? One add one is one, zero.

So what do you think I'm going to do next? I'm going to put the one in the underneath bit.

The zero where it should be and I've crossed off the other one 'cause now I've sorted that one so I can cross it out.

So now I'm ready to do this next part.

So one add one, going back to our rule there.

One add one is one, zero.

So what am I going to do next? What do you think? Because there's nothing there on the left I can just put it straight on that line.

So one, zero, zero, zero would be the answer.

And again, we can double-check it.

Five add three is eight.

So you've got five on that first row.

Three, because two add one is three.

Five add three is eight.

And then you can just double-check that your answer there is eight and it is because that one is in the eight column.

So I've got it right.

So are you with me so far? Now, if you're not, please, please, please go back now.

Don't look at the next bit, 'cause the next bit is taking it a little bit further.

So don't look at that next bit if you didn't understand what I've just shown you.

If you didn't understand what I've just shown you, go back.

See if you can make a prediction about what I'm going to come up with next and how it actually works.

Even follow along with your pen and paper as well.

Get that table drawn and see if you can figure it out, too.

But don't move on until you've understood that last bit, all right? So just pause now and rewind, if you need to.

I'm going to move on now.

We're now going to start looking at how you deal with more ones.

And you've got more ones, 'cause it starts to get a little bit complicated when you get more and more ones to work out.

So let's try this one.

We've got one, one, one, add one, one.

So start off, nice and easy.

We know how to do this.

So one add one, look at the rule, is one, zero.

So we put the one below the line in the next column.

And then we just put that zero in the column that we're on.

But then when we get to the next column, hmm, it's got one add one add one this time.

And if we go to our rule, one add one add one is one, one.

So we do a similar thing this time.

We've just got more ones to deal with.

We put the one under the next column so that it's ready for the next bit.

And then we put the one in the current column that we're on and you can see that because I've moved on and I've worked out the other one, I've put a cross through it, Just to remember that I've worked that one out.

Now we're left with just one, one.

And we go back to that other rule.

One add one is one, zero, and we've got nothing left on that left hand side.

So we can just put the one, zero straight there.

So one, one, one, add one, one is one, zero, one, zero.

I wonder if you know already what one, zero, one, zero is.

I wonder if you've done it enough time now to know straight away in your head that it's 10.

Takes a little while, but that's quite an easy one to recognise.

So seven add three is 10 and you can just double-check your maths that you've done it right.

Well, you've got one, oh, one, oh in that bottom one.

So that's definitely 10 there.

And then you can just add your ones above it to make sure.

So four add two add one is seven.

And two add one is three.

Sorry, yeah.

Seven add three is 10.

So we know we've got it right, because we've converted it to decimal.

Double-checked our maths to make sure that it's accurate.

What I want you to do then now.

Hopefully I've helped you enough there, but if I haven't, please go back and look at the examples, okay? There's no point stressing yourself out trying these, if you still don't get it.

So just go back and keep watching it and it will sink in eventually, I promise you, okay.

So, but if you're ready, start having a go at these questions now.

Here's the solutions then.

So A was one, oh, one.

B was one, oh, oh, one.

C was 1,001.

Not, not 1,001.

I've got to be careful, one, zero, zero, one.

D was one, zero, one, zero.

And E was one, one, zero, zero, one.

So hopefully you've got those right.

We're now we're going to look at something called binary shifting.

You might think, oh, this sounds really tricky.

It really isn't tricky, okay.

So binary shifting is shifting the bits to the left or to the right.

If we shift to the left, then we multiply.

If we shift to the right, then we divide.

And you can even sing a silly song to help you remember this.

♪ So if we shift to the left, we multiply.

♪ ♪ But if we shift to the right, we divide ♪ Was that too cool for you? Sorry, sorry.

Sorry if I embarrassed you then.

So what we're going to do is we're going to take a look at this example.

So I want to multiply one, zero, zero by one, zero.

So by two, basically.

Now I'm going to do some binary shifting.

I'm going to multiply it.

Which way did we go for multiply? We go left.

So I shift the bits to the left by one place.

So take a look at the one there and you'll see it moved.

So it just gets moved over like that.

So if we want to double-check this, we can do it in decimal as well, 'cause four times two is eight.

And if we have a look, we've got one, zero, zero times one, zero is one, zero, zero, zero, which is also eight.

So if we shift our bits to the left once, then we have multiplied by two or by one, zero.

You can use binary shifts to multiply by two, four, eight, 16, however many steps you go.

If you want to multiply by four, then you shift left by two spaces.

Like so, 'cause you're timesing it by two and then you're timesing it by two again.

So you just shift it along.

So four times four is 16, that's in decimals.

So we can do our double-check.

But one, zero, zero times one, zero, zero, which is four, is one, zero, zero, zero, zero.

So we can double-check that.

So it was originally four, so one, zero, zero.

We shifted it over two spaces.

And now that one is in the 16 column.

So we know definitely got it right.

So if we shift to the left, we can multiply.

A good way to remember is the numbers get bigger as you go to the left, don't they? So that would help you understand that left is multiplying.

So let's try one.

One, one, one times one, zero, zero, zero.

So what's one, zero, zero, zero in decimal? It's an eight.

So I know this because how many shifts do you need to get from one to eight? This will help you sort of figure out how many shifts you've got to do.

So if I start at one, how many shifts to the left do I need to make before I get to eight? So I've got one shift, two shift, three shifts.

So if I make three shifts, then I'm going to have multiplied by eight.

So let's try it.

So we've got one, one, one there in its position.

This means that we need to shift our bits three spaces to the left.

So off we go.

And they've been shifted three spaces to the left and notice that we filled in with zeroes where we've shifted it across as well.

So one, one, one times one, zero, zero, zero is one, one, one, zero, zero, zero in binary.

We know that we've shifted it to the left three times to multiply by eight, but let's just double check that in our decimal numbers.

One, one, one is seven in decimal.

And one, zero, zero, zero is eight in decimal.

So seven times eight is 56.

And have we landed on 56? Well, 32 plus 16 plus eight is 56.

So we've definitely got it right.

So which direction do you shift to multiply? Left , okay.

Let's remember that it's left, multiply to the left.

Now you can also use binary shifting for divide.

So in order to divide, we do the same thing, but we step to the right this time.

So I've forgotten which way is right and which way is left.

So that's right.

Yeah.

Right, I'm getting so confused with my fingers 'cause my camera's the opposite way round.

So that's right, isn't it? But for me, it's left.

But that's for you, that's right.

So in order to divide, we do the same thing, but we step to the right this time.

So let's try this one.

One, zero, zero divide by one, zero.

So divide it by two.

So how many times do you think we need to shift? We are dividing by two.

So we shift to the right by one place.

So divide by two, shift to the right by one place.

And there we go.

We've moved it to one place.

We can double-check it.

We were originally on four.

We're dividing it by two.

Four divided by two is two.

And it's landed as one, zero.

Which is two.

So we've definitely got it right.

Always doing those conversions back to decimal.

It's always going to help me double-check.

Let's try another one.

So you've got one, zero, one divided by one, zero, zero.

So what's one, zero, zero in decimal? It is four.

So if we are going to shift to the right, if we're going to divide by four, how many shifts do we have to do? So here we are dividing by four.

So we need to shift the values to the right by two places this time.

So there we go.

And if we have a look at that, five divided by four is not quite one.

So let's just have a look at that.

In binary shifting, we can only work with whole numbers, any remainders are actually discarded.

So if we do the same division with our decimal number, then we are left with a decimal value.

If we did five divide by four on our calculator, it would tell us the answer was 1.

25, but we can't have 1.

25 in binary.

We can only have one.

So those values are discarded as they are shifted.

So which direction do you shift to divide this time? It's right, isn't it? So we're going to do some binary shifting and you're going to try it yourself now.

Remember, draw that table.

That table is so, so, so important and helpful.

So don't forget to have that table there.

You might want to have it with several rows underneath it, so you can add all your questions in there.

So first of all, you're going to multiply, then you're going to do your division as well.

So pause the video while you have a go at that.

And here are your solutions.

So pause the video while you take a look at those solutions and you mark your work.

Brilliant.

So that was quite a lot this lesson, wasn't it? It was quite intense.

So you did some practise as well from your conversions.

You did some counting in binary.

You did some addition in binary too, and then you did binary shifting and I'll hope you're all going to do that silly dance that I did to help you remember.

If not, don't worry.

You don't have to.

I'm not going to force you to do that.

Nobody needs to embarrass themselves like that.

So I really hope that you've got a lot out of this lesson.

And if you find it a little bit tricky, it's worth just doing the lesson again, just to really get it to stick in your mind, because it is quite tricky.

All these little things that you have to remember to do with binary to decimal and addition and shifting and things.

It's a lot to remember.

So it's okay if you need to go back and just have a little look again, that's fine.

If you'd like to, please ask your parent or carer to share your work on Instagram, Facebook, or Twitter, tagging at Oak National and hashtag #LearnwithOak.

And you can show me your silly dance, or you can show me how many you got right in your little quizzes that you did.

That would be a nice thing to share, wouldn't it? Now, I'll see you again soon for lesson four.