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## Computing in the Modern World Data Representation

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### Computing in the Modern World Data Representation Wayne Summers STEM Honors Camp June 8, 2012 – PowerPoint PPT presentation

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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)

7
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
• 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
edvkyztYavfFMs
• Codecs
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