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Lots of Bits

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Title: Lots of Bits


1
Lots of Bits
  • Representations and Moores Law

2
http//www.2wheelbikes.com/sitebuilder/images/cabl
e-lock-comb-bike-accessories-469x345.jpg
3
How many bit strings of length n?
  • Adding one bit doubles the number

4
Text
  • 8 bits per character
  • A 01000001
  • ( 00101000
  • How many combinations of 8 bits?
  • 2 2 2 2 2 2 2 2 28 256

5
Hexadecimal Digits
6
ASCIIAmerican Standard Code for Information
InterchangeCharacter represented by Hex xy, e.g.
4B is K
7
ASCII Underneath
  • Emails
  • Web pages

8
http//farm4.static.flickr.com/3021/2494096946_2bf
86f8571.jpg?v0
9
What if you need more than 256 characters?
  • Unicode
  • 32 bits per character

10
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14
How many Unicode characters?32 bits each, so
there are in all

15
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16
Binary counting1110, or 110 and carry 1
17
Positive and Negative Numbers
  • Signed and unsigned numbers
  • Unsigned 28256 bit patterns represent 0 255
  • Signed 28 bit patterns represent -128 127
  • Leftmost bit sign bit 0 gt 0 or pos, 1 gt neg
  • Largest 8-bit positive number 01111111 127
  • 0 00000000
  • Most negative negative number
  • 10000000 -128

18
Negative numbers
-1 11111111so addition works the same for
positive and negative numbers
19
Biggest Numbers
  • Biggest positive number 01111111 (like 999999
    on a car odometer)
  • Most negative negative number 10000000

20
Biggest Positive Number 1 Most Negative
Negative Number
OVERFLOW!
21
The Comair Christmas Glitch
  • 16 bits for monthly count of crew changes
  • Biggest positive 16-bit number 32,767
  • December was a bad month, lots of snowstorms,
    lots of flights rescheduled
  • As Christmas approached the count went from
    32,767 to -32,768 by adding 1

22
Bytes
  • 1 byte 8 bits 2 hex digits 1 character
  • 210 1024 bytes 1 kilobyte 1KB
  • 220 1,048,576 bytes 1 megabyte 1MB
  • 230 bytes 1 gigabyte 1GB a billion
  • 240 bytes 1 terabyte 1TB a trillion
  • 250 bytes 1 petabyte 1PB a quadrillion
  • 260 bytes 1 exabyte 1EB a quintillion bytes
  • 270 zetta
  • 280 yotta

23
K
  • All this terminology based on the accident that
  • Which is 1K?
  • There are new standard names
  • 1 kibibyte 1000 bytes
  • vs. 1 kilobyte 1024 bytes
  • But almost no one uses kibi-, mebi-, etc.


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26
Moores Law (1965)
  • The number of transistors on a silicon chip
    doubles every 18 or 12, or 24 months
  • 1965 64 26
  • 2008 2 billion 231
  • 25 doublings in 43 years one doubling every 20
    months

27
Example of linear increase
28
Example of exponential increase
  • Now for the y axis use instead lg(y) the
    exponent e such that 2ey

29
Same plot, using lg(y) instead of y
30
One of the Greatest Engineering Achievements
  • An increase by a factor of 225 is about 30
    millionfold
  • If human speed had increased that much over the
    past 43 years, we would now be traveling faster
    than the speed of light
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