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

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COUNTING IN BINARY Binary weightings 0 x x x x 8

COUNTING IN BINARY Binary weightings 0 x x x x 8

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Presentation transcript:

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)

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

… 9 Using decimal numbers to count stones

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

? One more stone

Zero, carry 1 10

20

23

29

30

99

100

250

,00010,000100,000 Number positions …

x 100 = x 10 = 50 0 x 1 = 0 250

Mayan base 20 glyphs

Binary: base 2Hexadecimal: base 16

A B C D E F

A B C D E F … … 255 FF Decimal counting Hexadecimal counting … Binary counting

Binary number positions …

A binary example x 32 = 32 0 x 16 = 0 1 x 8 = 8 1 x 4 = 4 0 x 2 = 0 1 x 1 = 1 45

,09665,536 1,048,576 Hexadecimal number positions …

A hexadecimal example 3 6 B 3 x 256 = x 16 = 96 B x 1 =

Base 20 Base 10 Base 16 Base 2 Summary

Self study questions 1.If I am counting in binary, what is plus 1? 2.If I am counting in binary, what is 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 (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?

Links Mayan numbers: Hindu-Arabic number system: