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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