1. Representation of Data in Computer Systems
Units
Representation of Data in Computer Systems

2. Activity 1
5 minutes to research the following:

3. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Introduction
In this unit we will understand the importance and versatility of binary numbers and how binary is used to store data in computer systems.
Numbers
Text
Images
Sound
Instructions
…are all stored in binary and we will understand how this is done!

4. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
How can images, text & sound be made up of binary numbers? It is fairly easy to understand how numbers are stored in binary format in computer systems. But what about text, images and sound? The key thing to remember is that text, images and sound are all converted into numbers before they are stored in computers in binary form.

5. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Why Binary? Computers are made up of switches. They are either on (1) or off (0). Computers therefore cannot physically represent any more than 2 numbers (0 and 1) So any type of data that the computer deals with HAS to be converted into a binary number for the computer to process it.

6. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
So to recap…
What are the different types of data can be represented by computer systems?
Numbers, text, images (inc moving) and sound
What has to happen to these types of data before they can be processed by the computer?
Converted to numbers
Why can’t computer systems deal with numbers, text, images and sound in the form they are naturally in?
Computers can only handle 0’s and 1’s

7. What is Binary?
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
So What is Binary? Because humans have 10 fingers, we count using a denary number system (base 10): We count to ten… Then we record it by placing a 1 in the 10s column… …and when we get to 100, we make a record of it by placing a 1 in the 100s column…and so on!
Tens
Ones 2 1 4 3 2 5 1 4 6 9 7 8 4 5 1 2 3 5 9 6 8 6 9 2 3 1 7 7 8

8. What is Binary? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 …and so on!
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
So What is Binary? This is how we (like computers) count in binary We count to 2… Then we record it by placing a 1 in the 2s column… …and when we get to 2 sets of 2s, we make a record of it by placing a 1 in the 4s column…and so on!
Sixteens
Eights
Fours
Twos
Ones 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
…and so on!

9. Units of a Single Binary Number

10. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of a single binary number:
In the binary system we have some special names that we give binary numbers of different length.
The basic unit is 0 or 1.
This is a binary digit….also known as a
bit
A bit can store one of 2 numbers (0 and 1)

11. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of a single binary number:
A group of 8 bits is known as a…
Byte
A byte can store one of 256 numbers
128 64 32 16 8 4 2 1

12. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of a single binary number: Why do computer scientists use bytes? Traditional CPUs had registers which could hold a maximum of 8 bits. So each piece of data that came into the CPU would be 8 bits in length (representing a number from 0 to 255). A byte therefore became the standard size for a binary number… it can of course be greater but CPUs have set sized registers limiting the size of binary numbers that can be handled by its registers. 1 1

13. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of a single binary number:
A group of 4 bits (1/2 a byte) is known as a…
nibble 8 4 2 1

14. Units of Groups of Binary Numbers

15. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of sets/groups of binary numbers
Just like the traditional number system, binary also use the word kilo to represent (eg: kilogram = 1000grams)
But, 1000 is not a very neat binary number, so we go to its closest ‘neat’ value…
210 = 2x2x2x2x2x2x2x2x2x2 = 1024
210 29 28 27 26 25 24 23 22 21 20
1024
512
256
128 64 32 16 8 4 2 1

16. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of sets/groups of binary numbers So 1024 is at the heart of the way we group larger binary numbers…
8 bits
1 byte
8 (0’s / 1’s)
1024 bytes
1 kilobyte
Roughly 1000 bytes
8192 (0’s / 1’s)
1024 kilobytes
1 megabyte
Roughly 1 million bytes
8,388,608 (0’s / 1’s)
1024 megabytes
1 gigabyte
Roughly 1 billion bytes
8,589,934,592 (0’s / 1’s)
1024 gigabytes
1 terabyte
Roughly 1 trillion bytes
8,796,093,022,208 (0’s / 1’s)
1024 terabytes
1 petabyte
Roughly 1 quadrillion bytes
9,007,199,254,740,992 (0’s / 1’s)

17. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of sets/groups of binary numbers
A few binary numbers
Few bytes
Few kilobytes (kb)
Few Megabytes (mb)
Few Gigabytes (gb)
A few thousand binary numbers
A few million binary numbers
A few billion binary numbers

18. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of Single Binary Numbers On your whiteboard: Display a bit Display a byte Display a nibble

19. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Units of sets of Binary Numbers On your whiteboard: How many bytes are in a Kilobyte? 1024 (roughly 1000) Roughly how many bytes are in a Gigabyte? Roughly 1 billion What would be a sensible unit for the size of a music file? Megabytes What would be a sensible unit for the size of a persons surname? Bytes

20. Representing Numbers

21. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Converting Binary Numbers In your exam you will be expected to be able to convert a denary number (the numbers humans work with (base 10) into binary… …and back again.
128 64 32 16 8 4 2 1
157

22. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Converting from Binary to Denary (easy)
If you are given a binary number which is to be converted into denary do the following:
Above each bit, write the value of that bit.
Then simply add the values where there is a 1 underneath, together.
128 64 32 16 8 4 2 1 1 2 8 4 3 1

23. Representation of Data in Computer Systems
Learning Objectives:
Understand…
Units:
bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte
how data needs to be converted into a binary format to be processed by a computer.
Converting from Binary to Denary (easy)
128 64 32 16 8 4 2 1

24. Tasks
(10000 mins)
Create an A4 sheet outlining the different units that are given to
Single binary numbers
Sets of binary numbers