s kills : counting using any number system c oncepts : positional number systems, base (radix)
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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Skills: counting using any number systemConcepts: positional number systems, base (radix)
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Counting (number systems)
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Where does this topic fit?
• Internet concepts– Applications– Technology– Implications
• Internet skills– Application development– Content creation– User skills
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0 1 2 3 … 9
Using decimal numbers to count stones
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__
5 European
Arabic-Indic
Persian and Urdu
Hindi
Tamil
Mayan
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?
One more stone
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Zero, carry 1
10
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20
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23
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29
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30
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99
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100
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250
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110100
1,00
0
10,0
00
100,
000
Number positions
…
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110100
228
2 5 0
2 x 100 = 2005 x 10 = 500 x 1 = 0 250
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Mayan base 20 glyphs
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Binary: base 2 Hexadecimal: base 16
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0 1 0 1 2 3 4 5 6 7 8 9 A B C D E F
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0123456789101112131415161718192021
0123456789ABCDEF101112132425… …
255 FF
Decimal counting
Hexadecimal counting
01101110010111011110001001101010111100110111101111100001000110010100111010010101…11111111
Binarycounting
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12481632
Binary number positions
…
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12481632A binary example
1 0 1 1 0 1
1 x 32 = 320 x 16 = 01 x 8 = 81 x 4 = 40 x 2 = 01 x 1 = 1 45
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116256
4,09
6
65,5
36
1,04
8,57
6
Hexadecimal number positions
…
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116256
A hexadecimal example
3 6 B
3 x 256 = 7686 x 16 = 96B x 1 = 11 875
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Base 20 Base 10
Base 16Base 2
Summary
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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?
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Links
Mayan numbers:http://en.wikipedia.org/wiki/Maya_numerals
Hindu-Arabic number system:http://en.wikipedia.org/wiki/Hindu-Arabic_numeral_system