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

Skills: counting using any number systemConcepts: positional number systems, base (radix)

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Counting (number systems)

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0 1 2 3 … 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

110100

1,00

0

10,0

00

100,

000

Number positions

…

110100

228

2 5 0

2 x 100 = 2005 x 10 = 500 x 1 = 0 250

Mayan base 20 glyphs

Binary: base 2 Hexadecimal: base 16

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

0123456789101112131415161718192021

0123456789ABCDEF101112132425… …

255 FF

Decimal counting

Hexadecimal counting

01101110010111011110001001101010111100110111101111100001000110010100111010010101…11111111

Binarycounting

12481632

Binary number positions

…

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

116256

4,09

6

65,5

36

1,04

8,57

6

Hexadecimal number positions

…

116256

A hexadecimal example

3 6 B

3 x 256 = 7686 x 16 = 96B x 1 = 11 875

Base 20 Base 10

Base 16Base 2

Summary

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?

Links

Mayan numbers:http://en.wikipedia.org/wiki/Maya_numerals

Hindu-Arabic number system:http://en.wikipedia.org/wiki/Hindu-Arabic_numeral_system