Number Numbness 1

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 2

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 3

Binary Basis

Dec. 8 4 2 1

• 0 0 0 0 0• 1 0 0 0 1• 2 0 0 1 0• 3 0 0 1 1• 4 0 1 0 0• 5 0 1 0 1• 6 0 1 1 0• 7 0 1 1 1

Dec. 8 4 2 1

• 8 1 0 0 0• 9 1 0 0 1• 10 1 0 1 0• 11 1 0 1 1• 12 1 1 0 0• 13 1 1 0 1• 14 1 1 1 0• 15 1 1 1 1

Number Numbness 4

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 5

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 6

How Much Does it Cost

• 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 7

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 8

Size of Data Objects (2)

(pixel is short for Picture Elements)

Analog Television Picture 250,000 pixels

HDTV Picture 2,073,000 pixels

One Newspaper Photo 1,000,000 pixels

One Good 35 mm. Photo 10,000,000 pixels

Human Eye 60,000,000 pixels

Number Numbness 9

Size of Data Objects (3)

Photocells in the Human Eye 6.0 X 107

McDonald's Hamburgers sold 3.0 X 1010

Brain Cells in the Human Brain 1.0 X 1011

Hemoglobin mol. in the body 6.0 X 1014

Electrons in the Sun 1.0 X 1055

Number Numbness 10

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.