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Digital Cameras
 How the heck do they work?
Two kinds of camera
              Traditional       Digital

    See
                 Lens            Lens
the subject
 Record
                 Film           CCD
the image
  Store
                 Film         Binary data
the image
 Display      Print, after
                             On-board LCD
the image     processing
Two kinds of camera
              Traditional       Digital

    See
                 Lens            Lens
the subject
 Record
                 Film           CCD
the image
  Store
                 Film         Binary data
the image
 Display      Print, after
                             On-board LCD
the image     processing
Two kinds of camera
              Traditional       Digital

    See
                 Lens            Lens
the subject
 Record
                 Film           CCD
the image
  Store
                 Film         Binary data
the image
 Display      Print, after
                             On-board LCD
the image     processing
Two kinds of camera
              Traditional       Digital

    See
                 Lens            Lens
the subject
 Record
                 Film           CCD
the image
  Store
                 Film         Binary data
the image
 Display      Print, after
                             On-board LCD
the image     processing
Two kinds of camera
              Traditional       Digital

    See
                 Lens            Lens
the subject
 Record
                 Film           CCD
the image
  Store
                 Film         Binary data
the image
 Display      Print, after
                             On-board LCD
the image     processing
What is a CCD?

•   Charged Couple Device

•   Made up of hundreds of
    thousands of photocells

•   Each cell receives energy in
    the form of light and converts
    it to a mathematical value
Visual data = mathematical data?
0   0   0   0   0   0   0   0   0   0
0   1   1   0   0   0   0   1   1   0
0   1   1   0   0   0   0   1   1   0
0   0   0   0   0   0   0   0   0   0
0   0   0   0   1   1   0   0   0   0
0   0   0   1   1   1   1   0   0   0
0   1   0   0   0   0   0   0   1   0
0   0   1   0   0   0   0   1   0   0
0   0   0   1   1   1   1   0   0   0
0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0
0   1   1   0   0   0   0   1   1   0
0   1   1   0   0   0   0   1   1   0
0   0   0   0   0   0   0   0   0   0
0   0   0   0   1   1   0   0   0   0
0   0   0   1   1   1   1   0   0   0
0   1   0   0   0   0   0   0   1   0
0   0   1   0   0   0   0   1   0   0
0   0   0   1   1   1   1   0   0   0
0   0   0   0   0   0   0   0   0   0
0000000000
0110000110
0110000110
0000000000
0000110000
0001111000
0100000010
0010000100
0001111000
0000000000
Each bit of data is a pixel, or picture element.
                0000000000
                0110000110
                0110000110
                0000000000
                0000110000
                0001111000
                0100000010
                0010000100
                0001111000
                0000000000
When we record more data, we’re adding resolution.
                  0000000000
                  0110000110
                  0110000110
                  0000000000
                  0000110000
                  0001111000
                  0100000010
                  0010000100
                  0001111000
                  0000000000
10 pixels wide x 10 pixels tall = 100 pixels
20 pixels wide x 20 pixels tall = 400 pixels
400 pixels is four times as much resolution.
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   0
0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   0
0   0   0   0   1   1   0   0   0   0   0   0   0   0   1   1   0   0   0   0
0   0   0   0   1   1   0   0   0   0   0   0   0   0   1   1   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
What about color images?
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   1   1   1   1   0   0   0   0   0   0   0   0   1   1   1   1   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   0
0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   0
0   0   0   0   1   1   0   0   0   0   0   0   0   0   1   1   0   0   0   0
0   0   0   0   1   1   0   0   0   0   0   0   0   0   1   1   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   0   0   0   0   1   1   1   1   1   1   1   1   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
In color photographs, each pixel records three colors.
   0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0
       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0       0  0
   0 0 0 0         0 0 0 0         0 0 0 0         0 0 0 0         0 0 0 0         0 0 0 0         0 0 0 0         0 0 0 0         0 0 0 0         0   0 0 0
     0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0
   0   0 0 0       1   0 1 0       1   0 1 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   0 1 0       1   0 1 0       0   0 0 0
     0    0          1    1          1    1          0    0          0    0          0    0          0    0          1    1          1    1          0    0
   0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0
     0    0          1    1          1    1          0    0          0    0          0    0          0    0          1    1          1    1          0    0
   0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0
     0    0          1    1          1    1          0    0          0    0          0    0          0    0          1    1          1    1          0    0
   0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0
     0    0          1    1          1    1          0    0          0    0          0    0          0    0          1    1          1    1          0    0
   0   0 0 0       0   1 0 1       0   1 0 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   1 0 1       0   1 0 1       0   0 0 0
     0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   0 1 0       1   0 1 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          0    0          1    1          1    1          0    0          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          0    0          1    1          1    1          0    0          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       1   0 1 0       1   1 1 1       1   1 1 1       1   0 1 0       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          1    1          1    1          1    1          1    1          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       1   1 1 1       1   1 1 1       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          1    1          1    1          1    1          1    1          0    0          0    0          0    0
   0   0 0 0       1   0 1 0       0   0 0 0       0   1 0 1       0   1 0 1       0   1 0 1       0   1 0 1       0   0 0 0       1   0 1 0       0   0 0 0
     0    0          1    1          0    0          0    0          0    0          0    0          0    0          0    0          1    1          0    0
   0   0 0 0       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       0   0 0 0
     0    0          1    1          0    0          0    0          0    0          0    0          0    0          0    0          1    1          0    0
   0   0 0 0       0   1 0 1       1   0 1 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   0 1 0       0   1 0 1       0   0 0 0
     0    0          0    0          1    1          0    0          0    0          0    0          0    0          1    1          0    0          0    0
   0   0 0 0       0   0 0 0       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       0   0 0 0       0   0 0 0
     0    0          0    0          1    1          0    0          0    0          0    0          0    0          1    1          0    0          0    0
   0   0 0 0       0   0 0 0       0   1 0 1       1   0 1 0       1   0 1 0       1   0 1 0       1   0 1 0       0   1 0 1       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          1    1          1    1          1    1          1    1          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       1   1 1 1       1   1 1 1       1   1 1 1       1   1 1 1       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          1    1          1    1          1    1          1    1          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       0   1 0 1       0   1 0 1       0   1 0 1       0   1 0 1       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0
   0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0       0   0 0 0
     0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0
       0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0          0    0

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Digital Cameras

  • 1. Digital Cameras How the heck do they work?
  • 2. Two kinds of camera Traditional Digital See Lens Lens the subject Record Film CCD the image Store Film Binary data the image Display Print, after On-board LCD the image processing
  • 3. Two kinds of camera Traditional Digital See Lens Lens the subject Record Film CCD the image Store Film Binary data the image Display Print, after On-board LCD the image processing
  • 4. Two kinds of camera Traditional Digital See Lens Lens the subject Record Film CCD the image Store Film Binary data the image Display Print, after On-board LCD the image processing
  • 5. Two kinds of camera Traditional Digital See Lens Lens the subject Record Film CCD the image Store Film Binary data the image Display Print, after On-board LCD the image processing
  • 6. Two kinds of camera Traditional Digital See Lens Lens the subject Record Film CCD the image Store Film Binary data the image Display Print, after On-board LCD the image processing
  • 7.
  • 8.
  • 9.
  • 10.
  • 11. What is a CCD? • Charged Couple Device • Made up of hundreds of thousands of photocells • Each cell receives energy in the form of light and converts it to a mathematical value
  • 12. Visual data = mathematical data?
  • 13.
  • 14.
  • 15. 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  • 16. 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  • 18. Each bit of data is a pixel, or picture element. 0000000000 0110000110 0110000110 0000000000 0000110000 0001111000 0100000010 0010000100 0001111000 0000000000
  • 19. When we record more data, we’re adding resolution. 0000000000 0110000110 0110000110 0000000000 0000110000 0001111000 0100000010 0010000100 0001111000 0000000000
  • 20. 10 pixels wide x 10 pixels tall = 100 pixels
  • 21. 20 pixels wide x 20 pixels tall = 400 pixels
  • 22. 400 pixels is four times as much resolution. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  • 23. What about color images? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  • 24. In color photographs, each pixel records three colors. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0