1. Digital Information Storage Contents: Binary vs decimal Advantages of binary CDs and DVDs

2. Binary: TOC 0 1 2 3 4 5 6 7 8 9 10 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 Bin to Dec: 1101 = 1 x2 3 + 1 x2 2 + 0 x2 1 + 1 x2 0 = 13 Place 128 64 32 16 8 4 2 1 Dec to Bin: 237- 1 x1281 - msb 109- 1 x641 45 - 1 x321 13 - 0 x160 13 - 1 x81 5 - 1 x4 1 1 - 0 x20 1 - 1 x11 - lsb 237 = 11101101 237 to binary:

3. Whiteboards: Binary Conversions 11 | 2 | 3 | 4234 TOC

4. W Convert 11001 to decimal: 25 11001 = 1 x2 4 + 1 x2 3 + 0 x2 2 + 0 x2 1 + 1 x2 0 = 25

5. W Convert 11011010 to decimal: 218 11011010 = 1 x2 7 + 1 x2 6 + 0 x2 5 + 1 x2 4 + 1 x2 3 + 0 x2 2 + 1 x2 1 + 0 x2 0 = 218

6. W Convert 175 to binary: 10101111 175: Place 128 64 32 16 8 4 2 1 Dec to Bin: 175- 1 x1281 - msb 47 - 0 x640 47 - 1 x321 15 - 0 x160 15 - 1 x81 7 - 1 x4 1 3 - 1 x21 1 - 1 x11 - lsb 175 = 10101111

7. W Convert 198 to binary: 11000110 198: Place 128 64 32 16 8 4 2 1 Dec to Bin: 175- 1 x1281 - msb 70 - 1 x641 6 - 0 x320 6 - 0 x160 6 - 0 x80 6 - 1 x4 1 2 - 1 x21 0 - 0 x10 - lsb 198 = 11000110

8. Advantages of Binary TOC Analog storage: Signal varies continuously Ex – magnetic tape Degradation Taping a record or CD Digital storage: 1 vs 0 less subtle Degradation Copying a CD Error Correction

9. Analog to digital conversion (ADC) TOC Sample rate/depth Same basic approach that we took for dec to bin soundcards…

13. CDs sample at 44,100 Hz, 16 bit depth

14. Information Storage on a CD TOC 0 1 Pass around CD Drive

15. Pits change laser path length (destructive vs constructive) 2d = 1 / 2 λ Example – if the pits are 150 nm deep, what wavelength of laser light will create destructive interference relative to this depth? 2d = 1 / 2 λ 2(150 nm) = 1/2λ λ = 600 nm

16. Rayleigh Criterion  = r = 1.22 d b  = Angle of resolution (Rad) r = min distance separating pits (m) d = distance to CD from lens (m) = Wavelength of laser (m) b = Diameter of CD Lens (m) DVDs ≈ 640 nm CDs ≈ 780 nm Central maximum of one is over minimum of the other

17. 8 bits bytes are actually mapped to 14 bits on CDs

18. Whiteboards: Pits and interference 11 | 2 | 323 TOC

19. W If an optical drive uses light that is 340 nm, what pit depth would create destructive interference? 85 nm 2d = 1 / 2 λ = 1 / 2 (340 nm) d = 85 nm

20. W A CD has pits that are 125 nm deep. What wavelength of laser light would generate destructive interference relative to that depth? 500 nm 2(125 nm) = 1 / 2 λ λ = 500 nm

21. W Example: DVDs have pits that are about 0.74μm apart. If the lens has a diameter of 4.2 mm, and the laser has a wavelength of 780 nm, what must be the maximum distance from the lens to the disc so that the reader can resolve the pits? 3.3 mm  = r = 1.22 d b d = (0.74E-6)(4.2E-3)/(1.22*780E-9) =.003266…

22. Other methods of data storage RAM/cache Flash memory/Core Magnetic CD/DVD