Lesson video

Hello.

My name is Mrs. Jones and I'm really pleased you decided to join this lesson today.

In this lesson, we will look at how we use different symbols, what binary digits are, and why we use them in today's use of technology.

So let's get started.

Welcome to today's lesson.

Today's lesson is called Binary Digits from the unit, Data representation: text and numbers.

And by the end of this lesson, you'll be able to explain what binary digits are and calculate the bits required to represent a sequence.

There are two key words to today's lesson.

Binary.

Binary is a number system that uses two distinct symbols, the digit 0 and 1, to represent a number.

It's also called base two bit.

Bit.

Bit s a binary digit, the basic unit of data within a computer system that has the value 0 or 1.

There are three parts to today's lesson.

The first is explain binary digits, the second, calculate bits required to represent a sequence, and the third explain why computers use binary.

So let's start with explain binary digits.

What do we call these symbols? How many of them are there? We have the letters there of the alphabet.

We call these symbols letters.

There are 26 of them.

Sequences of letters form words.

What is the length of this word? How many symbols does it contain? The length is three letters.

Can you give another example of a three-letter word? Examples could be dog, hen, pet, or any valid sequence of three letters.

What do we call these symbols? How many of them are there? Zero, one, two, three, four, five, six, seven, eight, nine.

We call these symbols digits.

There are 10 of them.

Sequences of digits form numbers.

What is the length of this number? How many symbols does it contain? The length is three digits.

Can you give another example of a three-digit number? Well, examples could be 123, 890, 007.

Simply select a digit from 0 to 9 three times.

How many three-digit numbers can there possibly be? 10 times 10 times 10 is 10 to the power of three, which equals 1,000 or possible three digit numbers.

What do we call these symbols, 0, 1? How many of them are there? We call these symbols binary digits and there are only two of them.

Binary digits are often called bits and it comes from the word binary, B-I from binary and T-S from the end of digits.

We put those together to get bits.

Bits are symbols just like letters and digits.

Bits are the symbols that digital devices use to do their writing.

See there we have the letters, digits, and binary digits.

Let's have a quick check.

Binary digits are often called.

a, bytes, b, bits, c, digits.

Pause the video to consider your answer and then we'll check it.

Let's check your answer.

The answer was b, bits.

Well done if you got that correct.

At the lowest level, computers only process data as binary, sequences of bits, 0 or 1.

Ultimately, computers use sequences of symbols, 0s and 1s, to represent all types of information.

Let's have a quick check.

What is the length of this sequence? 101.

How many symbols does it contain? Pause the video to consider your answer and then we'll go through it.

Let's check your answer.

The length is three binary digits or three bits.

Can you provide another example of a three-bit sequence? Pause the video, consider another three-bit sequence and then we'll check your answer.

Let's check your answer.

Could be 111 could be 110 could be 000.

Simply select zero or one three times.

Well done if you got that correct.

How many three-bit numbers can there possibly be? Pause the video to consider your answer and then we'll check it.

Let's check your answer.

2 times 2 times 2 equals 2 to the power of 3, which equals 8 possible three-bit sequences.

Well done if you got that correct.

Let's do an activity.

There are two parts.

What are the only two binary digits? And the second, what is a bit? Pause the video, go back through the slides, use your worksheet, and then we'll check your answers.

<v ->Let's check your answers.

</v> <v ->The first question, what are the only two binary digits?</v> Well, the two binary digits are 0 and 1.

And the second part was, what is a bit? A bit is short for binary digit.

It's the smallest unit of data in a computer and can be either a 0 or a 1.

Well done if you've got that correct.

Let's move to the second part of today's lesson.

Calculate bits required to represent a sequence.

Text messages, SMS, user a coding scheme similar to ASCII.

It is called GSM 03.

38 and represents each character with a sequence of seven bits.

How many binary digits does it take to represent the message, "See you tonight!"? Well, each character is represented by seven bits.

There are 16 characters in the message.

Aisha says, "I only count 14 characters." Lucas says, "I think we have to include the spaces too, Aisha." Really good points.

7 times 16 equals 112 bits for the whole message.

Let's have a quick check.

A single text message is restricted.

It must contain fewer than 1,120 bits.

What is the maximum number of characters a single text message can have? Pause the video, consider your answer, and then we'll check it.

Let's check your answer.

How many seven bit sequences can fit into 1,120 bits? 1,120 divided by 7 equals 160 characters in a single text message.

Well done if you got that correct.

How many one-bit sequences can there possibly be? Two, one bit, 0 or 1.

How many two-bit sequences can there possibly be? Four, twice the number of one-bit sequences.

How many three-bit sequences can there possibly be? Eight, twice the number of two-bit sequences.

Let's have a quick check.

What happens each time we add an additional bit? A, the number of possible bit sequences doubles.

B, the number of possible bit sequences triples.

C, the number of possible bit sequences halves.

Pause the video to consider your answer and then we'll check it.

Let's check your answer.

The answer was a, the number of possible bit sequences doubles.

Well done if you've got that correct.

Telegraphy.

It is a way of sending messages over long distances using wires, electrical signals or radio waves.

In telegraphy, each character was encoded using a sequence of five bits.

This image is from a real cheat sheet for the international telegraph alphabet and shows how all of 32 possible sequences of five bits were used in the code.

There is obviously no room for both lowercase and uppercase letters or digits or symbols.

To solve this problem, almost all sequences have two symbols associated with them, a 'letter' and a 'figure'.

So any sequence could mean two different things, depending on whether the transmission was in 'letter' or 'figure' mode.

Two special sequences were used to switch between 'letter mode' and 'figure mode', similar to pressing Shift on a keyboard.

Let's have a quick check.

In telegraphy, each character was encoded using a sequence of five bits.

How many five-bit sequences can there possibly be? Is that sufficient to encode letters, digits, and symbols? Pause the video to consider your answers and then we'll check them.

Let's check your answers.

For the first part, it's 2 to the power of 5, which is 32 possible five-bit sequences.

And the second part is 26 letters, 52 for both cases, 10 digits and over 20 symbols.

Five bits are not sufficient.

Well done if you've got those correct.

Let's do an activity.

Let's explore what happens as we create longer and longer sequences of binary digits.

ASCII uses sequences of seven bits to represent characters.

The first part is how many different characters can be encoded using seven bits? The second part is, are seven bits sufficient for encoding lowercase and uppercase letters, digits and symbols, and explain why.

The third part is, many eight-bit coding schemes are based on seven-bit ASCII.

Using an additional bit doubles the number of possible characters.

Why do you think it was necessary to extend the original seven-bit code with an additional binary digit? Pause the video, use your worksheet, go back through the slides, and then we'll go through the answers.

Let's check your answers.

For the first question.

How many different characters can be encoded using seven bits? There are 2 to the power of 7, which equals 128 different seven-bits sequences, so ASCII can encode up to 128 different characters.

The second question was, are seven bits sufficient for encoding lowercase and uppercase letters, digits and symbols? Explain why.

Uppercase plus lowercase is 52 characters.

Digits, there are 10 characters.

Common symbols is approximately 20 characters.

Therefore, yes, 128 characters are sufficient for letters, digits, and symbols.

The third question was, why do you think it was necessary to extend the original seven-bit code with an additional binary digit? With an eight-bit coding scheme, there can be 256 different characters.

The additional 128 characters can be used to represent the characters of a second language, alongside the English characters.

Well done if you've got those correct.

Let's move to the last part of today's lesson.

Explain why computers use binary.

Aisha says, "But why do computers use 0 and 1?" Good question.

Lucas says, "Could we not use any two other symbols?" We could have picked any other pair of symbols.

There is nothing special about them.

But 0 and 1 are convenient for representing numbers.

Why use just two symbols? Why not 10, or 26, like humans? Building binary systems is simpler.

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

Each switch is binary, it has two possible states.

Let's do a quick check.

True or false? Switches are binary because they have three possible states.

Pause the video to consider if that is true or false and then we'll check your answer.

Let's check your answer.

The answer was false.

Pause the video to consider why that is false and then we'll go through the answer.

Let's check your answer.

Each switch is binary because it has two possible states, on and off.

Well done if you got that correct.

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

The switches can take various forms and you can see some examples here of relay switches from 1840, vacuum tubes or valves from 1940, and transistors from 1950.

Let's do a quick check.

Fill in the blanks to complete the sentence.

Electronic blank are built using blank of interconnected blank that control the flow of electricity.

And you have three possible words, switches, devices, circuits.

Pause the video to consider where each word goes in that sentence and then we'll check your answer.

Let's check your answer.

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

Well done if you got that correct.

Electronic devices are made from circuits containing lots of connected switches that manage the flow of electricity.

Today, these circuits use switches made from silicon and they're packed tightly together in small chips.

Inside these chips, there are billions of switches connected in complex patterns and each switch is now only a few atoms wide.

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

This is what happens in your computer's processors, CPU, GPU, main memory, RAM, storage devices, SD cards, SSDs, and any electronic component.

Let's do an activity and you'll need your worksheet.

In your own words, explain why computers use binary.

Pause the video to consider your answer.

Use your worksheet, go back through the slides, and then we'll check it.

Let's check your answer.

Computers use binary because they work using electrical signals.

Each part of a computer can only be in one of two states, on, represented by a 1, off, represented by 0.

Binary is a number system that uses only two digits, 0 and 1.

This makes it perfect for computers because it matches how the hardware works.

Using sequences of 0s and 1s, computers store and process all kinds of data like text, images, sound, and video.

Well done if you got that correct.

In summary, binary digits or bits are the smallest unit of data in computing.

They can only be a zero or one.

Bits are used to represent information such as letters, numbers, or colours using just 0s and 1s.

You can measure the size of binary data by counting how many bits it contains.

The more bits you have available, the more information you can store or represent.

Well done for completing this lesson on binary digits.