DATA STORAGE

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DATA STORAGE

• Tian-Li Yu
• tianliyu_at_cc.ee.ntu.edu.tw
• Department of Electrical Engineering
• National Taiwan University

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Binary world

• Bit binary digit (0/1)
• Simple, logical, and unambiguous
• Boolean operations gates

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Logical gates

• Logical world vs. real world
• To be or not to be ? always true

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Flip-flop

• Purpose to keep the state of output until the
  next excitement.
• Has an input line which sets its stored value to
  1
• Has an input line which sets its stored value to
  0
• While both input lines are 0, the most recently
  stored value is preserved

Flip-flop
x
z
y
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A simple flip-flop circuit
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Another flip-flop
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Hexadecimal coding (hex)

• 001100101100
• ? 32C

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Main memory cells

• Cell A unit of main memory (typically 8 bits
  which is one byte)

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Main memory address
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Memory techniques

• Random Access Memory (RAM) Memory in which
  individual cells can be easily accessed in any
  order
• Static Memory (SRAM)
• Dynamic Memory (DRAM) Tiny capacitors
  replenished regularly by refresh circuit
• Synchronous DRAM (SDRAM)
• Capacity
• Kilobyte 210 bytes 1024 bytes 103
• Megabyte 220 bytes 1,048,576 bytes 106
• Gigabyte 230 bytes 1,073,741,824 bytes 109

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Mass Storage

• Magnetic Systems (Disk, Tape)
• Optical Systems (CD, DVD)
• Flash Drives
• Larger capacity
• Less volatility
• Slower
• On-line or off-line

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Magnetic disk storage system

• Head, track, sector, cylinder
• Access time Seek time Rotation delay/latency
  time
• Transfer rate (ATA 100/133, SATA 1.5/3.0, etc)

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CD storage
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Physical vs. logical records
Files File systems
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Buffer

• A memory area used for the temporary storage of
  data (usually as a step in transferring the
  data).
• Blocks of data compatible with physical records
  can be transferred between buffers and the mass
  storage system.
• Data in buffer can be referenced in terms of
  logical records.

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Representing Text

• ASCII (American standard code for information
  interchange by ANSI) 7 bits (or 8 bits with the
  1st bit 0)
• Unicode 16 bits
• ISO standard (International organization of
  standardization) 32 bits

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ASCII example
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Representing Numeric Values
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From binary to decimal
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From decimal to binary
131x231x220x211x20
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Representing images

• Bit map techniques
• Pixel picture element
• Colors RGB, HSV, etc.
• LCD, scanners, digital cameras, etc.
• Vector techniques
• Scalable
• TrueType, PostScript, SVG (scalable vector
  graphics), etc.
• CAD, printers

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Representing sounds

• Sampling MIDI (synthesis)

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Binary system revisited

• Addition
• Subtraction? Lets define negative number first.

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Twos complement notation
For x positive, x ? x -x ? (2n x)
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Encoding negatives (2s complement)
Another way binary encoding (2n y) for 2s
complement (-y)
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Subtraction in 2s complement
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Excess notation system
Conversion x ? (2n-1 x) mod 2n
Addition xy ? (2n-1(2n-1 x)(2n-1 x)) mod 2n
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Overflow

• Addition of two positive numbers
• 23 5 ? -3 (mod 8)
• Addition of two negative numbers
• (-2) (-3) -5 ? 3 (mod 8)

010 ) 011 ---------- 101
110 ) 101 ---------- 011
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Fraction in binary
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Floating-point notation

• Why? (how to represent 0.0000000000001?)

Usually excess notation
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Decoding floating-point

• 01101011
• (0) (110) (1011)
• .1011 ? 10.11 ? 2 ½ ¼ 2¾

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Truncation errors
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Normalized form

• The most significant bit of mantissa is 1
• 0s floating-point representation is all 0s.
• 01100011 ? (0) (110) (0011) ? .0011 x 22
• ? .1100 x 20 ? (0) (100)(1100) ? 01001100

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Loss of digits

• 4 ¼ ¼ 011110000011100000111000
• 01111000 0111000001110000
• 01111000 4 !!!
• 4 (¼ ¼) 01111000(0011100000111000)
• 01111000 01001000
• 01111000 01110001
• 01111001 4½ !!!
• How to use calculator to do (1099 0.123 1099)?

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Data compression

• Lossy vs. lossless
• Run-length encoding
• Frequency-dependent encoding
• Huffman codes
• Relative encoding / difference encoding
• Dictionary encoding
• Adaptive dictionary encoding
• LZW encoding

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Huffman encoding

• AAABBBAABCAAAABD
• A?00 B?01 C?10 D?11
• 000000010101000001100000000111 (32 bits)
• A ? 0 B?10 C?110 D?111
• 0001010100010110000010111 (25 bits)

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LZW encoding

• xyx xyx xyx xyx
• 1
• 12
• 121
• 1213
• 12134
• 121343434
• x ? xy ? xyx ? xyx xyx xyx xyx

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Images, audios, and videos

• GIF 256 colors, dictionary encoding
• JPEG
• Lossy or lossless
• Discrete cosine transform
• Discard high-frequency information that is
  insensitive to human eyes
• MP3
• temporal masking
• Frequency masking
• MPEG
• Relative encoding other techniques

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Parity Bits

• Communication
• RAID (Redundant Array of Independent Disks)
  Techniques

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Error-correcting codes
Maximized hamming distances between symbols (at
least 3)
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Exercises

• No hand-in
• Ch 1.1 4, 6, 7
• Ch 1.3 6
• Ch 1.5 3, 4
• Ch 1 3, 30, 31, 32, 44, 53, 54, 60