Counting number systems Skills counting using any number

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.

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

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

One more stone ?

Zero, carry 1 10

20

23

29

30

99

100

250

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

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

Mayan base 20 glyphs

Binary: base 2 Hexadecimal: base 16

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

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

1 2 4 8 16 … 32 Binary number positions

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

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

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

Summary Base 20 Base 10 Base 2 Base 16

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 aa 3 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?

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