🎯 Learning Objectives
Develop the Data & Data Representation Learning Strands:
- Convert between different units and multiples of representation size.
- Find out what bytes are, and what the prefixes kilo-, mega-, giga- and tera- mean.
- Provide examples of the different ways that binary digits are physically represented in digital devices, including electricity, magnetism, light, and even holes in paper.
💬 Key Vocabulary
- representations
- representation size
- prefixes
- units
- binary digits
- multiples
📝 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?
📖 Bytes
A group of eight binary digits is called a byte.
In computing, it is very common to group binary digits into chunks of eight.
Caution
- Bit: 1 binary digit
- Byte: 8 binary digits
These are not the same.
Do not confuse them.
Example
Here are 8 binary digits:
00101101
This is 1 byte.
Here are 24 binary digits:
00101101
01000110
11110001
These are 3 bytes.
📖 Conversions: bits to bytes
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?
Answer
128 ÷ 8 = 16 bytes = 16 B
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
📖 Conversions: bytes to bits
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.
Answer
To convert bytes to bits:
multiply the number of bytes by 8
because there are 8 bits in every byte
🥈 Silver Badge – Bits and Bytes
📖 Reminder
All pieces of information are represented as sequences of binary digits.
Examples
- text ✓
- numbers ✓
- images
- sounds
- animations and videos
- programs
📖 Multiples
When we talk about a large quantity, the details are not important.
We use multiples such as thousands, millions, etc.
Example
We would never be interested in the fact that a song is 24,354,768 bits in size; this level of detail is not useful and can be cumbersome.
This is the case with large measurements in general, not just representation size. In most cases, it would be sufficient to describe the size of the representation as approximately 24 million bits long.
📖 Prefixes
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 |
📖 Translate and convert: use prefixes and bytes
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)
So this is how the size of a sequence which is 24 million binary digits long would be described: 3 MB
📖 Translate and convert: understand prefixes and bytes
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)
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
🥇 Gold Badge – Compare and convert
🥉 Platinum Badge – How do we store data?
Download the resource sheet below, read through it and then answer the questions and attempt the explorer tasks in the Microsoft Form below.
In this lesson, you…
Learnt how to handle bytes and prefixes and use them to talk about representation sizes.
Next lesson, you will…
Take a quiz that will allow us to assess what we’ve learned.
Play a game.