Transcript Number Game

Binary Numbers
• The binary system is the basis of the
numbers and symbols used in a computer.
• The reason is that binary numbers have just
two values (0,1) and computer switches and
logic gates also have two values (on,off)
• The following game works because of
binary numbers
Number Numbness
1
Number Game
Guess a number between 1 and 15. Which of
the following lists is it in:
 1 3 5 7 9 11 13 15
 2 3
6
7 10 11 14 15
 4 5
6
7 12 13 14 15
 8 9 10 11 12 13 14 15
Number Numbness
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Binary Basis
Dec. 8 4 2 1
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0
1
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5
6
7
0
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1
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Dec. 8 4 2 1
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Number Numbness
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15
 
1
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Number Numbness
Most people lose track of numbers that get too
large. They have no emotional link to the
meaning of numbers greater than a few
thousand.
The slides that follow might help to reconnect
us to these large numbers.
Number Numbness
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Number Numbness
Taken from Douglas Hofstadter's
“Metamagical Themas”
One Thousand
=
1,000
One Million
=
1,000,000
One Billion (U.S.)
=
1,000,000,000
One Trillion (U.S.)
= 1,000,000,000,000
One Billion (non U.S.) = 1,000,000,000,000
Number Numbness
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How Much Does it Cost
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How much does an automobile cost?
How much does a city bus cost?
How much does a baseball stadium cost?
How much does a Boeing 777 cost?
How much does an aircraft carrier cost?
How much does a space station cost?
Number Numbness
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Size of Data Objects (1)
One Video Display Screen
2,000 char.
One Newspaper page
30,000 char.
One "Floppy Disk"
1,000,000 bytes
U. W. M. Tape Library 10,000,000 gigabytes
U. W. M. Library
100,000 gigabytes
Number Numbness
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Size of Data Objects (2)
(pixel is short for Picture Elements)
Analog Television Picture
HDTV Picture
One Newspaper Photo
One Good 35 mm. Photo
Human Eye
250,000 pixels
2,073,000 pixels
1,000,000 pixels
10,000,000 pixels
60,000,000 pixels
Number Numbness
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Size of Data Objects (3)
Photocells in the Human Eye
McDonald's Hamburgers sold
Brain Cells in the Human Brain
Hemoglobin mol. in the body
Electrons in the Sun
Number Numbness
6.0 X 107
3.0 X 1010
1.0 X 1011
6.0 X 1014
1.0 X 1055
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Time Measurements
Age of the Universe
3.2 X 1017 sec.
One Galactic Year
6.4 X 1012 sec.
One Year on Jupiter
7.9 X 109 sec.
One Earth Year
3.2 X 107 sec.
One Earth Day
8.6 X 104 sec.
Human Response Time
1.0 X 10-1 sec.
Fastest computer cycle time 1.0 X 10-9 sec.
Spin time of the electron
1.0 X 10-20 sec.
Number Numbness
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