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S kills : counting using any number system C oncepts : positional number systems, base (radix)

Counting ( number systems). S kills : counting using any number system C oncepts : positional number systems, base (radix). This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License. . Where does this topic fit?. Internet concepts Applications

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S kills : counting using any number system C oncepts : positional number systems, base (radix)

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  1. Counting (number systems) 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.

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

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

  4. 5 European Arabic-Indic Persian and Urdu Hindi Tamil Mayan __

  5. One more stone ?

  6. Zero, carry 1 10

  7. 20

  8. 23

  9. 29

  10. 30

  11. 99

  12. 100

  13. 250

  14. Number positions … 100,000 10,000 1,000 100 10 1

  15. 228 2 x 100 = 200 5x 10 = 50 0x 1 = 0 250 100 10 1 2 5 0

  16. Mayan base 20 glyphs

  17. Binary: base 2 Hexadecimal: base 16

  18. 0 1 2 3 4 5 6 7 8 9 A B C D E F 0 1

  19. 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 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001 10010 10011 10100 10101 Decimal counting Hexadecimal counting Binary counting … … … 255 FF 11111111

  20. Binary number positions … 32 16 2 8 4 1

  21. A binary example 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 32 16 8 4 2 1 1 0 1 1 0 1

  22. Hexadecimal number positions … 1,048,576 65,536 4,096 256 16 1

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

  24. Summary Base 20 Base 10 Base 2 Base 16

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

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

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