1. Binary Aim: Explain binary and binary units Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa Objective 2: Add two 8-bit binary integers and explain overflow errors which may occur Objective 3: Define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte

2. talk to the hands! Binary What is a denary number? 234 Why Base 10?

3. Binary What is a binary number? Binary is the universal language of computers 1s248163264128 1100110100101010111101010100101110 10101111010101010101001011000101000 10001111100011010001000101001011101 Why Base 2?

4. Binary Converting denary to binary 234 1s248163264128 0001 234-128=106 1 106-64=42 1 42-32=10 11 10-8=2

5. Binary Converting denary to binary - EXERCISE Convert the following to 8 bit binary: 16 34 128 132 00010000 00100010 10000000 10000100 47 255 11 127 00101111 11111111 00001011 01111111

6. Binary Converting denary to binary – Online Game http://forums.cisco.com/CertCom/game/binary_game_page.htm

7. Binary Adding binary to binary Adding 8 bit binary numbers 00101010 + 01101101 1 0101010 0 0 101101 111110 1 0 1 0 1 THREE RULES! 0 + 0 = 0 0 + 1 = 1 1 + 1 = 0 (carry 1) 151 109 42 DEC

8. Binary Adding binary to binary Adding 8 bit binary numbers 10010110 + 10011011 0 0010110 1 1 011011 10 1 10 OVERFLOW! ERROR OVERFLOW! ERROR 0 1 0 1 1 1 01 305 155 150 DEC

9. Binary Adding binary to binary - EXERCISE 00010010 + 01000011 = 10000101 + 00111110 = 00101010 + 01101101 = 10010110 + 10001101 =

10. Binary Adding binary to binary - EXERCISE 00010010 + 01000011 = 1 0010010 0 0 000011 10 1 101010

11. Binary Adding binary to binary - EXERCISE 1000010 + 00111110 = 0 0000010 0 1 111110 00 1 110 1 0 1 0 1 0 1

12. Binary Adding binary to binary - EXERCISE 00101010 + 01101101 = 1 0101010 0 0 101101 11110 1 10 1 0 1

13. Binary Adding binary to binary - EXERCISE 10010110 + 10001101 = 0 0010110 1 1 001101 110 1 100 1 0 1 0 1 OVERFLOW!

14. Binary Tools to Help

15. Binary Units What is a bit? A bit can either be a 1 or 0

16. Binary Units What is a byte? A byte is 8 bits

17. Binary Units A nibble is 4 bits A nibble is half a byte What is a nibble? This is a mouse This This is a mouse This is a mouse

18. Binary Units A kilobyte is 1024 bytes What is a Kilobyte (KB)? x 1024 Why not 1000?

19. Binary Units What is a Megabyte (MB)? A megabyte is 1024 kilobytes

20. Binary Units What is a Gigabyte (GB)? A gigabyte is 1024 megabytes

21. Binary Units What is a Terabyte (TB)? A terabyte is 1024 gigabytes

22. Binary Units What is a Petabyte (PB)? A petabyte is 1024 terabytes

23. Binary Units - EXERCISE Arrange the following in size order: BIT BYTE NIBBLE KILOBYTE MEGABYTE GIGABYTE TERABYTE PETABYTE

24. Binary Aim: Explain binary and binary units Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa Objective 2: Add two 8-bit binary integers and explain overflow errors which may occur Objective 3: Define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte

25. Binary and Hexadecimal Web Resources LESSON FILES http://edmundo.ecis.org/downloads/ CISCO BINARY GAME http://forums.cisco.com/CertCom/game/binary_game_page.htm BINARY UNITS http://www.teach- ict.com/gcse_new/computer%20systems/storage_units/miniweb/index.htm

26. talk to the feet! Binary and Hexadecimal What is a hexadecimal number? Why Base 16?

27. Binary and Hexadecimal How are hexadecimal numbers used? MAC Address: 54-42-49-9B-6D-62 MAC Address (in binary): 1010100-1000010-1001001-10011011-1101101-1100010

28. Binary and Hexadecimal How are hexadecimal numbers used? WHITE #ffffffR255 G255 B25511111111 11111111 11111111 BLACK #000000R000 G000 B00000000000 00000000 00000000

29. Binary and Hexadecimal Converting denary to hexadecimal 74 / 16 = 4 (4 x 16 = 64) 74 74 - 64 = 10 10 = A 4A

30. Binary and Hexadecimal Converting denary to hexadecimal 255 / 16 = 15 (15 x 16 = 240) 255 255 - 240 = 15 15 = F FF

31. Binary and Hexadecimal Converting denary to hexadecimal - EXERCISE Convert the following to hexadecimal: 16 34 128 132 10 22 80 84 47 255 11 127 2F FF B 7F