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Computing in the Modern World Data Representation

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Title: Computing in the Modern World Data Representation


1
Computing in the Modern WorldData Representation
  • Wayne Summers
  • STEM Honors Camp
  • June 8, 2012

2
Data Representation
  • NUMBERS

3
(No Transcript)
4
Essential Questions
  • ? How can the two-state nature of transistors be
    used to represent information?
  • ? How are decimal numbers converted to binary
    numbers and vice versa?
  • ? What is the 8-bit ASCII code?

5
There are 10 kinds of people in the world those
who understand binary and those who dont.
6
Pre-exercises
  • Magic trick (parity bits) tack board with
    colored cards
  • Representing numbers Binary digit counting
    cards (1, 2, 4, 8, 16, 32)
  • Decimal, Binary, Hexadecimal

7
Decimal Binary Hexadecimal
1 0000 0001 1
2 0000 0010 2
3 0000 0011 3
4 0000 0100 4
5 0000 0101 5
6 0000 0110 6
7 0000 0111 7
8 0000 1000 8
9 0000 1001 9
10 0000 1010 A
11 0000 1011 B
12 0000 1100 C
13 0000 1101 D
14 0000 1110 E
15 0000 1111 F
16 0001 0000 10
8
Data Representation
  • LETTERS

9
Representing letters Letter card some words

10
(No Transcript)
11
Data Representation
  • IMAGES

12
Essential Questions
  • ? How is the binary system used to represent
    images?
  • ? What is a pixel?
  • ? How is a pixel used to represent images?

13
a. Describe how a picture is digitized and
represented in a computer.
14
Examples
  • http//www.printactivities.com/HiddenPictures/004_
    SunAndTree.html (paint by number picture per
    student)
  • What's the secret code for talking to spacecraft?
    - http//spaceplace.nasa.gov/binary-code/redirecte
    d/ (build poster)
  • RGB Hexadecimal / Decimal Converter -
    http//www.psyclops.com/tools/rgb/

15
Data Representation
  • SOUNDS

16
Essential Questions
  • ? How is the binary system used to represent
    sound?
  • What is a sound sample?
  • What is amplitude?
  • ? How is a sound sample used to represent a sound?

17
Sound Representation
  • Analog
  • Digital

18
Characteristics of Sound
  • Amplitude
  • Wavelength (w)
  • Frequency ( )
  • Timbre
  • v f
  • Hearing 20Hz 20KHz
  • Speech 200Hz 8KHz

19
Digital Representation of Audio
  • Must convert wave form to digital
  • sample
  • quantize

20
Sampling (in time)
  • Measure amplitude at regular intervals
  • How many times should we sample?

21
Example
  • Suppose we have a sound wave with a frequency of
    1 cycle per second

22
Example
  • If we sample at one cycle per second, where would
    the sample points fall?

23
Example
  • If we sample at 1.5 cycles per second, where will
    the sample points fall?

24
Sampling - Example
  • If we sample at two cycles per second, where do
    the sample points fall?

25
Nyquist Theorem
  • For lossless digitization, the sampling rate
    should be at least twice the maximum frequency
    response.
  • In mathematical terms
  • fs gt 2fm
  • where fs is sampling frequency and fm is the
    maximum frequency in the signal

26
Quantization
27
3-bit Quantization
A 3-bit binary (base 2) number has 23 8 values.
Amplitude
Time measure amp. at each tick of sample clock
28
4-bit Quantization
A 4-bit binary number has 24 16 values.
Amplitude
Time measure amp. at each tick of sample clock
A
29
The Digital Audio Stream
Its just a series of sample numbers, to be
interpreted as instantaneous amplitudes one for
every tick of the sample clock.
Previous example
11 13 15 13 10 9 6 1 4 9 15 11 13 9
This is what appears in a sound file, along with
a header that indicates the sampling rate, bit
depth and other things.
30
Common Sampling Resolutions
Word length Uses
8-bit integer Low-res web audio
16-bit integer CD, DAT, DV, sound files
24-bit integer DVD-Video, DVD-Audio
32-bit floating point Software (usually only for internal representation)
31
16-bit Sample Word Length
A 16-bit integer can represent 216, or 65,536,
values (amplitude points).
We typically use signed 16-bit integers, and
center the 65,536 values around 0.
32,767
0
-32,768
32
Audio File Size
CD characteristics
- Sampling rate 44,100 samples per second (44.1
kHz)
- Sample word length 16 bits (i.e., 2 bytes)
per sample
- Number of channels 2 (stereo) - Examples -
http//x2.i-dat.org/csem/UNESCO/1/index.htmlse
How big is a 5-minute CD-quality sound file?
33
b. Describe how a sound/song is digitized and
represented in a computer.
  • An audio file format is a container format for
    storing audio data on a computer system. They can
    be divided in three basic groups
  • uncompressed audio file formats,
  • lossless compression audio formats and
  • lossy compression audio file formats.

34
uncompressed audio file formats
  • The most used and known uncompressed audio file
    format is PCM (Pulse-code modulation)
  • usually stored as a .wav on Windows or as .aiff
    on MAC.
  • flexible file formats designed to store more or
    less any combination of sampling rates or
    bitrates.
  • CD-quality sound files in uncompressed PCM format
    are large in size - around 10 MB per minute.

35
lossless compression audio formats
  • require more processing for the same time
    recorded,
  • more efficient in terms of disk space used,
  • FLAC (Free Lossless Audio Codec) - audio format
    similar to MP3,
  • audio information is compressed file without any
    loss in its audio quality (similar to how Zip
    works)

36
lossy compression audio file formats
  • most used audio format today
  • best known is MP3 (MPEG-1 Audio Layer 3)
  • patented digital audio encoding format
  • common audio format for consumer audio storage,
    de facto standard of digital audio compression
    for the transfer and playback of music on digital
    audio players.

37
Sound links
  • The Digital Representation of Sound,Part One
    Sound and Timbre
  • Part Two Playing by the Numbers

38
Data Representation
  • MULTIMEDIA

39
Multimedia
  • combination of several media types
  • audio stream,
  • moving images (movie/video),
  • audiovideo,
  • animation,
  • interactive animation

40
Sample-based Digital Video
  • Video is represented in discrete units called
    frames
  • Frame Similar to a still image
  • Video has a frame rate unit frames/second (fps)
  • E.g., 15 frames/second
  • Time-dependent medium
  • Illusion of motion depends on frame rate
  • Dont perceive motion below about 15 fps

41
Video Frames
  • Each frame has a resolution (wwidth by h
    height)-- typically the same resolution for all
    the frames in video

w

42
Frame Rates
  • Movies fps 24
  • American TV (NTSC) fps 30
  • European TV (PAL) fps 25
  • Peter Jackson's The Hobbit fps 48 (5120-by-2700
    cameras)

43
Video and multimedia files
  • contain digitally capturing, recording,
    processing, storing, transmitting, and
    reconstructing a sequence of still images
    representing scenes in motion and of course
    captured or recorded audio.
  • basically data container formats, that are used
    for audio-with-video playback.

44
video file formats
  • AVI (Audio Video Interleave) developed by
    Microsoft. Audio or video content can be
    compressed with a wide variety of video or audio
    and video codecs
  • MPG (MPEG), developed by Moving Picture Experts
    Group. ISO standard used by many multimedia
    devices (DVD players, Blu-RAY, portable players,
    computers).

45
video file formats
  • MP4, MPEG-4 multimedia file format, contains
    encoded video and advanced audio coding
    (AAC)-encoded audio content.
  • MOV, a Apple QuickTime multimedia container
    format that can store one or more tracks of data
    such as video, audio, text, and effects.

46
Video Compression
  • How compression works
  • http//www.youtube.com/watch?featureplayer_embedd
    edvkyztYavfFMs
  • Codecs
  • http//www.youtube.com/watch?v_13PCNDO-pEfeature
    player_embedded

47
Data Representation
  • SOFTWARE

48
  • Machine Code
  • Start .org 8020
  • SEI
  • LDA 80
  • STA 0315
  • LDA 2D
  • STA 0314
  • CLI
  • RTS
  • INC D020
  • JMP EA31
  • 8020 78 0111 1000
  • 8021 A9 80 1010 1001 1000 0000
  • 8023 8D 15 03
  • 8026 A9 2D
  • 8028 8D 14 03
  • 802B 58
  • 802C 60
  • 802D EE 20 D0
  • 8030 4C 31 EA

49
QUESTIONS???
  • http//cs.ColumbusState.edu
  • cs_at_ColumbusState.edu
  • wsummers_at_ColumbusState.edu
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