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Power of Numbers

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					     LSP 121

The Power of Numbers
                    Conversions
• 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?

                   12 inches
       23 feet x
                    1 foot
                    Conversions
• At a French department store, the price for a
  pair of Levi jeans is 45 euros. What is that in
  U.S. dollars?

                $1.37
   45 euros x            = $61.65
                1 euro
               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?
                                                       1 yd2
   23 ft x 18 ft = 414 ft2                 414 ft2 x           = 46 yd2
                                                       9 ft2
              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!
                     Standardized Units
                                                           Weights
 • In the U.S., we still use:                              Grain (0.0648 gram)
                                                           Ounce
                                                           Pound
                                                           Ton
                                                           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.
                 Standardized Units
• 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
       Large Values
       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………………..
             Standardized Units?
  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)
            Binary Numbers
• 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?
               Binary Numbers
• 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
             Binary Numbers
• Let’s play a game. You are a cashier at your
  favorite store. How do you make $0.86 in
  change?
• What if you only have dimes, nickels and
  pennies?
• A good cashier always tries to use the biggest
  coins possible.
             Binary Numbers
• 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.
             Binary Numbers
• What is the decimal value of binary
  10010101?

• What is the binary value of decimal 83?

• Use a calculator?
             Binary Arithmetic
• Let’s add the following two binary values

  10011100
  01011010

• 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”
         Binary Representation
 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)
               Binary Representation
 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
              Binary Representation
   So pretty much everything we do technology-wise is
    binary
       Computer work
       Music
       Television
       Photography/video
       Telephones/cellphones
   Is there any major at DePaul that does not use
    computers or binary numbers?

				
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posted:4/21/2013
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