Lesson video

Hello, I'm Sara, your computing teacher for this unit representations.

This is lesson three of six.

You will need pen and paper to take notes.

Remember to switch off notifications and remove any distractions before you begin.

Pause the video, and when you are good and ready, we can begin the lesson.

In this lesson, you will examine symbols, 0s, and 1s in more detail.

Give these symbols a name, examine the significance of these symbols and discover why there's only two of them.

There are different representations of cat.

Which of these sequences of symbols is most likely to represent the text cat in a computing device? Give this a good think, pause the video, and have a good think.

That's right, number two, because symbols commonly used in computing, are 0s and 1s and we've seen this earlier.

We saw the ASCII coding system where every character on your keyboard is mapped to a 7-bit code of 0s and 1s.

So who decided on the ASCII mapping between characters and binary sequences? Pause to think.

I don't expect you to know the answer to this one, but have a pause.

Right, it was American National Standards Institute.

So what happened many years ago in the 60s, for instance, we had teleprinters, really simple machines.

So you type in a master in one end, it gets transmitted and it comes out on the other end.

The American standards Institute decided to come together to create a common code that everyone can use to interchange and send messages, so we're using the same language, so to speak.

So they came up with the American Standard Code for Information Interchange.

Now, you know that this is a 7-bit coding scheme.

So it means that you can have from zero to one to seven.

So you can have seven zeros, zero, zero, zero, seven times to seven ones.

One, one, one, seven times, for your binary bit numbers.

Now that meant you had 120 different possible characters.

That was sufficient for all the characters on our keyboards, be uppercase and lowercase characters, numbers, and symbols.

So this code soon became the standard in English speaking countries.

Now, do you think this was the case in all every country or all of the countries? Yes, you thought right.

It wasn't enough because we have 128 different characters, but in other languages like Arabic and Russian, you have a lot more to cater for.

It's time for you to get into your first task.

In this particular task, you will have to name the symbols you see.

Pause the video, get your pen and paper, and you can actually have a look and name symbols.

Well done for trying.

So what do we call this symbols and how many are there? It's time for you to have a go at your first task.

Well done for trying.

So what do we call these symbols then? We call this symbols letters.

And you did rightly know that we have 26 of these letters in the sequence of symbols.

So the sequences or any sequence of symbols, we pick from this group of 26 letters, can form words.

Now have a look at this, have a go at task two.

Now we're going to determine the length of the word, cat.

And I'd like you to give another example of a three letter word.

Again, pause the video and I'll see you when you've completed the task, Again, well done.

Right, the length of the word we knew, or you know, is three letters.

And you could have given any example of a three letter word, but I've got three there.

We've got dog, we've got hen, we got pet, but you could have given any word.

Now consider these set of symbols you see before you.

What are these symbols called? And how many symbols can you see on screen? Pause again and I'll see you when you've completed the task.

Now, let's look.

Symbols we know are called digits and there are 10 of them.

And we have a sequence of digits form numbers just like a sequence of letters can form words.

So here is task four for you.

This one's a counting one.

So you've got counting task there.

So what is the length of the number 314? So count the digits in the number 314.

Also give an example of a digit, a 3-digit number.

And also I would like you to think carefully, how many 3-digit numbers can there possibly be? It's time to pause the video and when you've completed the task, we can continue.

Well done for trying.

So, you know, the length of a number, like rightly counted it are 3-digits.

So you have a 3-digit number, which is 314.

You would have given another example.

It could be any example.

There are lots of examples to choose from such as 123, 890, 007, and it's endless.

Well, not endless, but the list is quite long.

Right.

So how many, 3-digit numbers can there possibly be? So you would have articulated and you'd have rightly spotted that you have numbers you can start from sequence 000, and go all the way down to 999.

So which means, you've got a thousand possible digits.

So if you think you've got nine digits, zero, one, two, three to nine, and there are 10 digits, you will also, as we're working in multiples of 10, if you have 000, all the way to 999, you'd have a thousand digits.

But here's how to calculate it.

This is more straightforward and easy way.

So we're working in base 10 because in our decimal system, we've got 10 digits, 0-9, which we just see.

Because we're working in base 10, hence we've got 10.

Now it's 10 to the cubed because we've got three digits to consider.

So 10 to the cube gives us 1000.

And that's how you get that.

In your last task, you did some counting and you counted digits, in a familiar number system, which is a decimal system, which we're used to see.

So now we're going to go more into binary digits.

You're going to learn some more about binary digits.

Firstly, what do we call the symbols, 0s and 1s.

Now, you know they're binary digits, but they'd been shortened to mean bits.

And just like decimal numbers, where we've got digits 0-9, and we've got a sequence of symbols in our letters A-Z, and our binary digits, there are only two symbols.

So binary digits are symbols that digital devices, like your computer, use to do their writing.

Counting in bits.

We've counted in decimal, so we're going to counting bits, binary digits.

In this example, we've got the binary digit, 101.

Just like we counted the length of 314, the length of the binary number we see on screen is three bits.

So you know that 101, when you count the binary digits, you've got three bits.

Three binary digits.

And examples of three binary digits are; 111, 110, and 000.

And you can keep counting.

Those are just three examples.

So how many 3-bit numbers can there possibly be? So we counted 314, how many 3-digit numbers we saw earlier, can there possibly be? We have the formula we use because we worked in base 10, decimal.

But now we're working in base 2, because there can only be two possible digits.

So we have to use the number two.

Because we want a 3-bit number, a 3-bit number, we're going to have 2 raised to power 3.

Just like we had 10 raised to power 3.

So in that case, we're going to have 2 x 2 x 2.

So you've only got eight possible 3-bit numbers or 3-bit sequences.

You are now going to see how Twitter encodes it's characters.

So Twitter is a social networking service that sits on digital devices.

So we're counting in bits.

Now Twitter uses it's encoded characters into 8-bit sequences.

So not 7-bits like we saw in ASCII.

On screen before you, it's a first message that was sent in 2006, on Twitter.

And it says, "Just setting up my Twitter." So we're going to see how many binary digits it takes to represent this message.

So let's have a look.

Right.

So if an 8-bit sequence, which means J when you type J, that gets encoded into an 8-bit number.

So same as U-S-T-S and all of the characters will be encoded into 8-bit numbers.

So how many binary digit does it take to represent this message? So counting, counting all of that message are 24 characters.

So 24 characters each 8-bit, all you need to do is do 24 x 8 and that gives, 192 bits.

And that's how Twitter encodes these characters.

Now it's time for you to count the bits.

In this task, you need to count how many binary digits it takes to represent the message, "See you tonight." Don't forget Twitter uses 8-bit coding scheme, but we're going to go back to ASCII now because that's what our computers, that's the standard that computers are used to.

And ASCII is a 7-bit code or 7-bit coding scheme.

So pause the video, and when you've completed, I'll see you and we can continue.

Right.

Well done.

So how many binary digits for see you tonight? Right.

The final or the total number of digits will be 112.

And how did you get that? We know they're 7 binary digits required for each letter.

And when you counted, you counted 16 characters, including spaces, don't forget spaces.

So 7 x 16 gives you 112 bits.

Right, more counting to be done.

There is further counting you need to do.

So here is this next task.

You need to work out the maximum characters in a single text message.

And the text message is restricted to 1,120 bits.

So how many, 7-bit sequences can fit into this 1000, if I can get this right, 1,120 bits.

Remember, we're working in ASCII.

Pause the video, and when you've completed your task, I'll see you.

Right, great work.

So the maximum number of characters in this message, can only be 160 characters.

And how do you find that? So you need to find how many 7-bits sequences can fit into 1,120.

And all you need do is divide 1,120 by 7, and that gives you your maximum of 160 characters all together allowable in a single text.

Now onto some exploration and counting sequences.

So let's explore what happens when we create longer and longer sequences of binary digits.

We're just going to start with 1-bit.

So how many 1-bit sequences can there possibly be? So we're working in binary.

So we're working with 1s and 0s, but we want just to 1-bit sequence.

So there can only be a 0 or 1.

So you can make two unique digits, or two unique numbers, 0 and 1.

Right.

So you've got there, 2-bits.

So what if we increased that to 2-bits? How many 2-bits sequences can there be? So in a 2-bit sequence, you can have a 00, you can have a 01, or 10 or a 11.

So that takes it to 4 twice the number of a 1-bit sequence.

Now let's take that up one notch.

So how many 3-bit sequences can there possibly be? I know you're saying to yourself, I know this I've seen this, yes, I know the answer.

That's correct.

You're absolutely right.

There are eight.

And you've seen this before, twice the number of 2-bit sequences.

So you can start from 000, to 001, and all the way to 111.

So what's the pattern then.

So with every additional bit, the number of the possible bits sequence doubles.

Now on to our next expiration.

In this example, you see a telegraphy system here.

We've seen an example of a representation called ITA2, in an earlier lesson.

So in telegraphy, each character was encoded using a sequence of 5 bits.

So how many 5-bits sequences can there possibly be? And is that sufficient to encode letters, digits and symbols.

So bear in mind, we've got 26 letters, 10 digits, and we've got quite a few symbols.

In telegraphy, you have seen that each character was encoded using a sequence of 5 bits.

So we're working in binary, binary digits.

So we're going to go with 2 'cause only two possible digits.

So we're going to have 2 as our base number.

So we're going to have 2 raised to power 5.

We know we're considering 5 bits or a 5-bits sequence.

So it's 2 to 5.

And if we do 2 x 2 x 2 x 2 x 2, that gives us 32.

So if that's sufficient then, I think, you know, the answer is no, because there are 26 letters in the alphabet.

And if you consider capital letters, lowercase letters, 10 digits, and over 20 symbols, that's not sufficient whatsoever, to encode the characters on our keyboard.

It's your turn again.

This time, you'll be counting a 7-bit sequence.

This is what you've got to do.

How many different characters can be encoded using 7 bits? The hint you've got there is, how many possible 7-bit sequences can there be? Pause the video and I'll see you when you've completed this task.

Well done for having a go.

Right.

We know that ASCII uses sequences of 7 bits to represent characters.

So how many different characters can be encoded using 7 bits? Let's find out.

We know we're working with base 2.

There can only be two possible answers or digits rather.

So we've got two digits.

Our base number is 2.

We've got a 7-bit sequence of 7-bit number.

So we're going to have to do 2 to the power 7, which gives you 128, when you work that out.

So if this enough to encode letters, digits, and symbols? Let's find out again.

We've got uppercase and lowercase letters and we've got 26 of each.

That gives us 52 letters all together to cater for.

Digits, we've got 10 digits.

And there are about 20 common symbols that we need to cater for.

So if you add those up, yes, is the answer.

120 characters are sufficient for letters, digits, and symbols.

Here's some more counting practise for you.

Counting an 8-bit sequence this time.

How many different characters can be encoded using 8 bits? And why do you think it was necessary to extend the 7-bit code or ASCII code by 1 bit? Have a good go, pause the video and I'll see you when you've completed.

Right.

Let's have a look at this now.

What's the solution? But before that, here's a small fact for you.

Many 8-bit coding schemes are based on 7-bit ASCII.

Now onto the solution.

You know that with an 8-bit coding scheme, there can be 256 different characters.

And how did we get that? You would have worked out that using an additional bit, doubles the number of possible characters there could possibly be.

So 128 possible characters for a 7-bit code x 2, gives you 256 different characters.

So then why do you think it was necessary to extend the original 7-bit code with an additional binary digit to virtually double the number of different possible characters? The additional 120 characters can be used for representing the characters of a second language alongside English language.

A second language like Arabic, Russian, or perhaps Chinese.

So that gives so much more option or options rather.

Why binary? Why 0 and 1? We could have picked any other pair of symbols.

Why those two? Why not 10 numbers and the 26 letters like we're used to using? You do know that binary has two possible states, 0 and 1, off and on.

So building binary systems is simpler and convenient for the computer.

You can build a binary system using circuits of interconnected switches.

Electronic devices are built using these circles of interconnected switches that control the flow of electricity.

Switches take many forms, and you're going to look at a couple.

The fast one, you can see a vacuum tubes.

Now vacuum tubes are made of glass with all of its air removed to create a vacuum.

And vacuum tubes control the flow of electricity.

And these were used at switches in very, very early computers built many, many years ago.

This has now been replaced by the modern transistors, which are much smaller.

They also control the amount of electric current and by controlling the amount of electric current, builds on the binary state of 0 and 1.

Electronic devices that use switches to control the flow of electricity are now made out of Silicon.

And these transistors can be tightly packed into billions and billions and billions or billions and billions of them can be tightly packed into a chip, like we can see on screen.

Now looking closely, this Silicon based switches are packed, you probably cannot see what the billions and billions of transistors there're not very visible to the naked eye.

So they're quite built in and you're not meant to see.

Quite built into some very intricate patterns.

And they're very small and quite minute, and kind of atomic, in a way, the size of an atom.

So your eyes are not meant to see them.

These are the intricate patterns that you can find in your computer.

So these goes to explain what happens inside your computer, when you've got your processes, your main memory, your storage, and all your electronic components.

You have reached the end of this lesson.

So well done.

In this lesson, you examine binary digits to a great detail.

You know now, that 0s and 1s, are called binary digits or bits.

All characters are represented using sequences of symbols.

And you did see that binary digits are like letters.

They're the symbols that computers write with, like we write with alphabets or our letters A-Z, and numbers 0-1.

You also know that computers use two symbols because they're built out of switches.

Computers have switches called transistors, which control the flow of electricity.

And we saw what switches were used also in very old computers.

So well done.

It would be nice to see some of the lovely work you have putting this lesson.

If you would like to share your work, please ask your parent or carer to share on Instagram, Facebook, or on Twitter @OakNational and #learnwithOak.

Hope to see you next lesson.