Skills: counting with decimal and binary numbersConcepts: using a binary code for representing numbers, positional number systems, number system base, number of symbols in a number system

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Representing numeric data with bits

Where does this topic fit?

• Internet concepts– Applications– Technology– Implications

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Encoding numeric data

Data type Decade

Numeric 1950s

Alphanumeric 1960s

Text 1970s

Image 1990s

Speech 2000s

Music 2000s

Video 2000, 2010s

0 1 2 3 … 9

Using decimal numbers to count stones

?

One more stone

Zero, carry 1

10

Add 1 to the 1’s position

11

123456789

101112141516171819202122...

90919293949596979899

100101...

11

Using binary numbers to count stones

101 100 101 110

0123456789

101112131415161718192021…

Counting with decimal and binary numbers

01

1011

100101110111

10001001101010111100110111101111

100001000110010100111010010101…

250

11111010

Convert 11111010 (binary) to decimal

1 x 128 = 1281 x 64 = 641 x 32 = 321 x 16 = 161 x 8 = 80 x 4 = 01 x 2 = 20 x 1 = 0

Total = 250

11111010 (binary) = 250 (decimal)

Mayan base 20 symbols

99 or 1100011

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. Write the number 12 (base 10) in binary

4. Write the number 1101011 (binary) in decimal.

5. If I were a Mayan, how would I write the number 25 (base 10)?

6. 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