Digital Information Storage Contents Binary vs decimal Advantages

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

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

Binary: 0 1 2 3 4 5 6 7 8 9 10 0001 0010

Binary: 0 1 2 3 4 5 6 7 8 9 10 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 Bin to Dec: 1101 = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 13 237 to binary: Dec to Bin: 237 -1 x 128 109 -1 x 64 45 - 1 x 32 13 - 0 x 16 13 - 1 x 8 5 - 1 x 4 1 - 0 x 2 1 - 1 x 1 237 = 11101101 Place 128 64 32 16 8 4 2 1 1 - msb 1 1 0 1 - lsb TOC

Whiteboards: Binary Conversions 1|2|3|4 TOC

Whiteboards: Binary Conversions 1|2|3|4 TOC

Convert 11001 to decimal: 11001 = 1 x 24 + 1 x 23 +

Convert 11001 to decimal: 11001 = 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 25 25 W

Convert 11011010 to decimal: 11011010 = 1 x 27 + 1 x 26 +

Convert 11011010 to decimal: 11011010 = 1 x 27 + 1 x 26 + 0 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 1 x 21 + 0 x 20 = 218 W

Convert 175 to binary: 175: Dec to Bin: 175 -1 x 128 47 -0

Convert 175 to binary: 175: Dec to Bin: 175 -1 x 128 47 -0 x 64 47 - 1 x 32 15 - 0 x 16 15 - 1 x 8 7 - 1 x 4 3 - 1 x 2 1 - 1 x 1 Place 128 64 32 16 8 4 2 1 1 - msb 0 1 1 1 1 - lsb 175 = 10101111 W

Convert 198 to binary: 198: Dec to Bin: 175 -1 x 128 70 -

Convert 198 to binary: 198: Dec to Bin: 175 -1 x 128 70 - 1 x 64 6 - 0 x 32 6 - 0 x 16 6 - 0 x 8 6 - 1 x 4 2 - 1 x 2 0 - 0 x 1 Place 128 64 32 16 8 4 2 1 1 - msb 1 0 0 0 1 1 0 - lsb 198 = 11000110 W

Advantages of Binary Analog storage: Signal varies continuously Ex – magnetic tape Degradation Taping

Advantages of Binary 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 TOC

Analog to digital conversion (ADC) Sample rate/depth Same basic approach that we took for

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

CDs sample at 44, 100 Hz, 16 bit depth

CDs sample at 44, 100 Hz, 16 bit depth

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

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

Pits change laser path length (destructive vs constructive) 2 d = 1/2λ Example –

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

Rayleigh Criterion = r = 1. 22 d b = Angle of resolution (Rad)

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

8 bits bytes are actually mapped to 14 bits on CDs

Whiteboards: Pits and interference 1|2|3 TOC

Whiteboards: Pits and interference 1|2|3 TOC

If an optical drive uses light that is 340 nm, what pit depth would

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

A CD has pits that are 125 nm deep. What wavelength of laser light

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

Example: DVDs have pits that are about 0. 74μm apart. If the lens has

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? = r = 1. 22 d b d = (0. 74 E-6)(4. 2 E-3)/(1. 22*780 E-9) =. 003266… 3. 3 mm W

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

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