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

Binary: TOC Bin to Dec: 1101 = 1 x x x x2 0 = 13 Place Dec to Bin: x msb x x x x x x x11 - lsb 237 = to binary:

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

W Convert to decimal: = 1 x x x x x2 0 = 25

W Convert to decimal: = 1 x x x x x x x x2 0 = 218

W Convert 175 to binary: : Place Dec to Bin: x msb x x x x x x x11 - lsb 175 =

W Convert 198 to binary: : Place Dec to Bin: x msb x x x x x x x10 - lsb 198 =

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

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

CDs sample at 44,100 Hz, 16 bit depth

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

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

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

8 bits bytes are actually mapped to 14 bits on CDs

Whiteboards: Pits and interference 11 | 2 | 323 TOC

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

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

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) = …

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