1. Skills: counting using any number system Concepts: positional number systems, base (radix) This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License. Counting (number systems)

2. Where does this topic fit? Internet concepts – Applications – Technology – Implications Internet skills – Application development – Content creation – User skills

4. 0 1 2 3 … 9 Using decimal numbers to count stones

5. __ 5 European Arabic-Indic Persian and Urdu Hindi Tamil Mayan

6. ? One more stone

7. Zero, carry 1 10

8. 20

9. 23

10. 29

11. 30

12. 99

13. 100

14. 250

15. 1 10 1001,00010,000100,000 Number positions …

16. 1 10 100 228 250 2 x 100 = 200 5 x 10 = 50 0 x 1 = 0 250

17. Mayan base 20 glyphs

18. Binary: base 2Hexadecimal: base 16

19. 0 1 0 1 2 3 4 5 6 7 8 9 A B C D E F

20. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 24 25 … … 255 FF Decimal counting Hexadecimal counting 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001 10010 10011 10100 10101 … 11111111 Binary counting

21. 1 248 16 32 Binary number positions …

22. 12 48 16 32 A binary example 1 0 1 1 x 32 = 32 0 x 16 = 0 1 x 8 = 8 1 x 4 = 4 0 x 2 = 0 1 x 1 = 1 45

23. 1 16 2564,09665,536 1,048,576 Hexadecimal number positions …

24. 1 16 256 A hexadecimal example 3 6 B 3 x 256 = 768 6 x 16 = 96 B x 1 = 11 875

25. Base 20 Base 10 Base 16 Base 2 Summary

26. Self study questions 1.If I am counting in binary, what is 11111 plus 1? 2.If I am counting in binary, what is 11111 plus 11? 3.If I am counting in hexadecimal, what is FFFFF plus 1? 4.If I am counting in hexadecimal, what is aa3 plus 3? 5.If I am counting in hexadecimal, what is FFFFF plus F? 6.Write the number 12 (base 10) in binary, hexadecimal and trinary (base 3) 7.Write the number 1101011 (binary) in decimal, hexadecimal and trinary. 8.If I were a Mayan, how would I write the number 550 (base 10)? 9.True or false – all odd binary numbers end in 1?

27. Links Mayan numbers: http://en.wikipedia.org/wiki/Maya_numerals Hindu-Arabic number system: http://en.wikipedia.org/wiki/Hindu-Arabic_numeral_system