1. Units Representation of Data in Computer Systems

2. Activity 1 5 minutes to research the following:

3. Representation of Data in Computer Systems 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! Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

4. Representation of Data in Computer Systems 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. Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

5. Representation of Data in Computer Systems 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. Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

6. Representation of Data in Computer Systems 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 Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

7. What is Binary? 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! 123 4 56 7 8 9 123 4 56 7 8 9 1 2 123 4 56 7 8 9 0 0 Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

8. What is Binary? 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! 1 0 1 1 0 1 0 01 1 0 1 1 0 00 1 1 0 1 1 00 1 10 1 100 0 0 …and so on! Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

9. Units of a Single Binary Number

10. Representation of Data in Computer Systems 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 b inary dig it ….also known as a bit A bit can store one of 2 numbers (0 and 1) Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

11. Representation of Data in Computer Systems Units of a single binary number: A group of 8 bits is known as a… Byte A byte can store one of 256 numbers Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 1286432168421 10011101

12. Representation of Data in Computer Systems 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. Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 10011001 11001010 10111001 00111000

13. Representation of Data in Computer Systems Units of a single binary number: A group of 4 bits ( 1/2 a byte ) is known as a… nibble Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 8421 1101

14. Units of Groups of Binary Numbers

15. Representation of Data in Computer Systems Units of sets/groups of binary numbers Just like the traditional number system, binary also use the word kilo to represent 1000. (eg: kilogram = 1000grams) But, 1000 is not a very neat binary number, so we go to its closest ‘neat’ value… 2 10 = 2x2x2x2x2x2x2x2x2x2 = 1024 Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 2 10 2929 2828 2727 2626 2525 2424 23232 2121 2020 10245122561286432168421

16. Representation of Data in Computer Systems Units of sets/groups of binary numbers So 1024 is at the heart of the way we group larger binary numbers… Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 8 bits1 byte8 (0’s / 1’s) 1024 bytes1 kilobyteRoughly 1000 bytes 8192 (0’s / 1’s) 1024 kilobytes1 megabyteRoughly 1 million bytes 8,388,608 (0’s / 1’s) 1024 megabytes1 gigabyteRoughly 1 billion bytes 8,589,934,592 (0’s / 1’s) 1024 gigabytes1 terabyteRoughly 1 trillion bytes 8,796,093,022,208 (0’s / 1’s)

17. Representation of Data in Computer Systems Units of sets/groups of binary numbers Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. Few bytes Few kilobytes (kb) Few Megabytes (mb) Few Gigabytes (gb) A few binary numbers A few thousand binary numbers A few million binary numbers A few billion binary numbers

18. Representation of Data in Computer Systems Units of Single Binary Numbers On your whiteboard: Display a bit Display a byte Display a nibble Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

19. Representation of Data in Computer Systems 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 Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa.

20. Representing Numbers

21. Representation of Data in Computer Systems 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. Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 1286432168421 10011101 157

22. Representation of Data in Computer Systems Converting from Binary to Denary (easy) If you are given a binary number which is to be converted into denary do the following: 1.Above each bit, write the value of that bit. 2.Then simply add the values where there is a 1 underneath, together. Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 1286432168421 10000101 128 4 1 133 1

23. Representation of Data in Computer Systems Converting from Binary to Denary (easy) Learning Objectives: Units: a) Define the term bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte. b) Understand that data needs to be converted into binary format to be processed by the computer. Numbers: a) Convert positive denary numbers (0-255) into 8-bit binary numbers and vice versa. 1286432168421 10110011 10001111 00111100 10111100

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