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Lesson 5:

Large quantities

Year 8 – Data Representations – Representations: from clay to silicon

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Discussion

Starter activity

We use nanometres to measure the size of molecules.

We use centimetres to measure the size of objects.

We use kilometres to measure the distances between cities.

Why do we use different units?

Discuss this with the person next to you.

As learners enter the class, there is a question displayed on a slide: “We use nanometres to measure the size of molecules. We use centimetres to measure the size of objects. We use kilometres to measure the distances between cities. Why do we use different units?”

This question is all about different units (for measuring the size of binary representations) and it will frame our use of multiples and prefixes in a more familiar context. It is important to stress throughout that using different measurement units and prefixes is common scientific practice, and it is not specific to computing.

Ask the learners to share their thoughts, but there is no need to actually provide an answer at this point. You will link back to this question at an appropriate point in the lesson.

Image source: https://en.wikipedia.org/wiki/Galaxy#/media/File:M82_HST_ACS_2006-14-a-large_web.jpg

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In this lesson, we will...

Objectives

Find out what bytes are, and what the prefixes kilo-, mega-, giga- and tera- mean.

We will also practise converting between them.

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Bytes

Activity 1

In computing, it is very common to group binary digits into chunks of eight.

Example

Here are 8 binary digits:

00101101

A group of eight binary digits is called a byte.

This is 1 byte.

Caution

Bit: 1 binary digit

Byte: 8 binary digits

These are not the same.

Do not confuse them.

Ask learners whether they have ever heard of the term ‘byte’. If they think they haven’t, ask about megabytes, gigabytes, or terabytes.

Explain that bytes are commonly used in computing to measure the length of bit sequences. One byte comprises 8 binary digits.

You could ask learners why they think it’s called a ‘byte’. If learners imagine a group of 8 bits as a (literal) bite of bits, then that might help them distinguish the two. You could use the mnemonic device “try a little BIT before you take a full BITE (BYTE)”.

The learners might want to know why a grouping of binary digits, such as a byte, is specifically 8 bits long and not another length, like 10 bits long. The issue is discussed in the relevant Wikipedia article [en.wikipedia.org/wiki/Byte] and the brief answer is that the number 8 simply prevailed historically over other groupings that had also been used. It is essentially arbitrary.

Here are some relevant quotes from that article:

“The size of the byte has historically been hardware dependent and no definitive standards existed that mandated the size – byte-sizes from 1 to 48 bits are known to have been used in the past. Early character encoding systems often used six bits, and machines using six-bit and nine-bit bytes were common into the 1960s.”

“The development of eight-bit microprocessors in the 1970s popularized this storage size.”

“Historically, the byte was the number of bits used to encode a single character of text in a computer”

Learners often use the terms ‘bits’ and ‘bytes’ interchangeably. Stress that they are distinct and not to be confused. Inform the learners that, in fact, ‘byte’ is a deliberate respelling of ‘bite’ to avoid accidental confusion with ‘bit’.

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Bytes

Activity 1

Example

Here are 24 binary digits:

00101101

01000110

11110001

A group of eight binary digits is called a byte.

These are 3 bytes.

Caution

Bit: 1 binary digit

Byte: 8 binary digits

These are not the same.

Do not confuse them.

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Conversions: bits to bytes

Activity 1

00110001001000000110001001111001011101000110010100100000011010010111001100100000001110000010000001100010011010010111010001110011

A group of eight binary digits is called a byte.

This is a sequence of 128 bits.

What is its size in bytes?

How many groups of 8 can you form with 128 bits?

128 ÷ 8 = 16 bytes = 16 B

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Conversions: bits to bytes

Activity 1

To convert bits to bytes:

divide the number of bits by 8

because this is how many groups of 8 bits, i.e. bytes, ‘fit’ in the sequence

bits

bytes

÷8

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Conversions: bytes to bits

Activity 1

00110001001000000110001001111001011101000110010100100000011010010111001100100000001110000010000001100010011010010111010001110011

A group of eight binary digits is called a byte.

A piece of text is 16 bytes long.

What is its size in bits?

There are 16 groups of 8 bits each.

16 ⨉ 8 = 128 bits = 128 b

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Conversions: bytes to bits

Activity 1

To convert bytes to bits:

multiply the number of bytes by 8

because there are 8 bits in every byte

bits

bytes

⨉8

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Bits and bytes

Activity 2

Count the bytes in a couple of simple problems.

Write the answers on your worksheet.

bits

bytes

÷8

⨉8

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Bits and bytes: answers

Activity 2

Count the bytes in a couple of simple problems.

Check your answers against the ones provided and correct any mistakes.

Ask a classmate if you are in doubt. If a classmate cannot help you, ask your teacher.

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Reminder

Activity 3

Examples

text ✓

numbers ✓

images

sounds

animations and videos

programs

All pieces of information are represented as sequences of binary digits.

110101111010011110100111010011110011101011110100111101001110100111100111010111101001111010011101001111001110101111010011110100111010011110011101011110100111101001110100

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Representation size

Activity 3

All pieces of information are represented as sequences of binary digits.

Sequences of binary digits tend to get really long.

How do we talk about these huge numbers of binary digits?

type of information	number of bits
a chapter in a book	a few thousand

a photograph a song	a few million

a film the human genome	a few billion

all the files on a computer all the files on Wikimedia	a few trillion

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Activity 3

When we talk about a large quantity, the details are not important.

We use multiples

such as thousands, millions, etc.

My favourite song is 24,354,768 bits!

My favourite song is 24 million bits!

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Prefixes

Activity 3

Scientists use prefixes to denote multiples of a unit.

Examples

3 thousand grams is

3 kilograms or 3 kg

8 million pixels is

8 megapixels or 8 MP

4.5 billion years is

4.5 gigayears

prefix	short	meaning
kilo-	K	thousands
mega-	M	millions
giga-	G	billions
tera-	T	trillions

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Translate and convert: use prefixes and bytes

Activity 3

It is common practice to:

Use prefixes instead of multiples,

i.e. replace millions with mega-

Use short forms, i.e. replace mega- with M and bits with a lowercase b

Convert bits to bytes

(and use an uppercase B for bytes)

My favourite song is 24 megabits, or 24 Mb.

My favourite song is 24 million bits!

My favourite song is 24 megabits.

My favourite song is

3 megabytes, or 3 MB.

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Translate and convert: use prefixes and bytes

Activity 3

So this is how the size of a sequence which is 24 million binary digits long would be described:

3 MB

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Translate and convert: understand prefixes and bytes

Activity 3

Let’s try it the other way too.

To really understand sizes,

translate and convert:

Expand short forms, i.e. use

giga- and bytes instead of G and B

Translate prefixes to multiples,

i.e. billions instead of giga-

Convert bytes to bits (if you need to)

My operating system is

2 GB or 2 gigabytes

My operating system is

2 billion bytes.

My operating system is

16 billion bits.

My operating system is

2 GB.

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Translate and convert: use prefixes and bytes

Activity 3

So this is what a size of 2 GB really means: it’s a sequence of

16 billion binary digits

Translating and converting will help you interpret what may seem like gibberish

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Compare and convert

Activity 4

Practise finding your way around units and prefixes.

Write the answers on your worksheet.

Use the conversion cheat sheet, if you need to.

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Compare and convert: answers

Activity 4

Practise finding your way around units and prefixes.

Check your answers against the ones provided and correct any mistakes.

Ask a classmate if you are in doubt. If a classmate cannot help you, ask your teacher.

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Homework

Study the different ways in which information is stored and transmitted in digital devices

Perform simple conversions with prefixes

Explorer tasks

Plus: any activities that you did not complete during this lesson

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Next lesson

Summary

In this lesson, we...

Learned how to handle bytes and prefixes and use them to talk about representation sizes.

Next lesson, we will...

Take a quiz that will allow us to assess what we’ve learned.

Play a game.