The Power of Numbers
• Convert 23 feet to inches
– We all know there are 12 inches to a foot, so
12 * 23 = 276 inches
– But what did we really do?
23 feet x
• At a French department store, the price for a
pair of Levi jeans is 45 euros. What is that in
45 euros x = $61.65
Chain of Conversion
• How many seconds in one day?
24 hours 60 min 60 sec
1 day x x x = 86,400 sec
1 day 1 hour 1 min
• You want to carpet your bedroom. It is 23 feet x 18
feet. How many square yards is that?
23 ft x 18 ft = 414 ft2 414 ft2 x = 46 yd2
Chain of Conversion
• To connect a computer to the Internet, the
computer needs an IP address. Currently
IP addresses are 32 bits in length. How
many addresses is that?
IP addresses are binary, so raise 2 to the 32nd power
Or 232 = 4,294,967,296
• If they assign 1000 addresses a day, how
long would those addresses last (in years)?
Chain of Conversion
232 addresses x 1 day/1000 addresses = 4,294,967.296 days
4,294,967.296 days * 1 year/365 days = 11767.03 years
Be careful! Don’t do: 232 addresses x 1000 addresses/1 day
The term addresses won’t cancel!
• In the U.S., we still use: Grain (0.0648 gram)
Long ton (2240 pounds)
Lengths Liquid measures
Inch Teaspoon Dry measures
Foot Tablespoon (3 t) Dry pint
Yard Fluid ounce (2 T) Dry quart
Rod (5.5 yards) Cup (8 fluid ounces) Peck (8 dry quarts)
Fathom (6 feet) Pint (16 fluid ounces) Bushel (4 pecks)
Furlong (1/8 mile) Quart (2 pints) Cord (128 cubic feet)
Mile Gallon (4 quarts)
Nautical mile (6076.1 feet) Barrel of petroleum (42 gals)
Classic College of Engineering “expression”: Units of measure will always be stated
in least likely terms. Example: Furlongs per fortnight.
• Most of the rest of the world uses the metric
system: Small Values
deci d 10-1 one-tenth
meter – length centi c 10-2 one-hundredth
gram – mass milli m 10-3 one-thousandth
second – time micro µ 10-6 one-millionth
liter - volume nano n 10-9 one-billionth
pico p 10-12 one-trillionth
Note: 2.3E+06 = 2.3 x 106
deca da 101 (ten) 4.6E-04 = 0.00046
hecto h 102 (hundred)
kilo k 103 (thousand) (such as 200 kbps transfer speed)
mega M 106 (million)
giga G 109 (billion)
tera T 1012 (trillion) unless………………..
What about computer memory?
Note: memory is based on binary so we use base 2
K = kilo (kilobytes) = 210 = 1024
M = mega (megabytes) = 220 = 1,048,576
G = giga (gigabytes) = 230 = 1,073,741,824
T = tera (terabytes) = 240 = 1,099,511,627,776
followed by peta, exa, zetta, yotta
• Some groups suggested we should call
these kibi, mebi, gibi, tebi, pebi, exbi (and
yes, zebi and yobi)
• Why should anyone learn binary?
• All music, video, data, and computer programs
are stored in computer memory/storage
• Computers are based on the binary number
system (on/off or 1/0)
• If your iPod / computer / flash drive has x
storage capacity, what does that mean?
• Before we discuss binary arithmetic, do you
really understand decimal arithmetic?
1024 = 1 x 103 + 0 x 102 + 2 x 101 + 4 x 100
• Binary numbers are the same, except
there are only 2 digits (0 and 1), and the
base is 2
10010 = 1 x 24 + 0 x 23 + 0 x 22 + 1 x 21 + 0 x 20
• Let’s play a game. You are a cashier at your
favorite store. How do you make $0.86 in
• What if you only have dimes, nickels and
• A good cashier always tries to use the biggest
• You are now working in a foreign country.
They don’t have quarters, dimes, or nickels;
they have 16 cent pieces, 8 cent pieces, 4 cent
pieces, 2 cent pieces, and pennies, and you
can only give out at most one of each coin!
• How do you make change for $0.14? $0.29?
• Let’s list these coins in order from highest on
the left to lowest on the right.
• What is the decimal value of binary
• What is the binary value of decimal 83?
• Use a calculator?
• Let’s add the following two binary values
• When a computer does arithmetic, it converts
all values to binary.
• This takes a little bit of time, which is why we
say “if you aren’t doing arithmetic with the
data, don’t declare it as type numeric”
When you type the letter “n” on the keyboard, it
converts it to an 8-bit binary value, based on the
ASCII character set.
So all Word documents are stored sequences of 8-bit
ASCII characters (called bytes)
All color images are composed of teeny-tiny dots
(pixels). Each pixel is composed of so much red, so
much green, and so much blue (RGB)
Music on iPods and such are stored in binary
Music is an analog waveform
the waveform is sampled at regular intervals
each sample is converted to a binary value (such as 8-bits)
the binary values are stored in memory
Talking on a cellphone/telephone is also binary
all voice is converted to binary in the same way that music
is converted to binary
So pretty much everything we do technology-wise is
Is there any major at DePaul that does not use
computers or binary numbers?