A3. Data Representation
Learning Outcomes:
- Distinguish between analog and digital data. State
applications or situations where conversion of analog to digital data is
required, or vice versa.
- Explain why IT uses digital data
- The
relationship between the number of bits and number of patterns/combinations available
should be mentioned (e.g. three bits can be used to represent eight colours).
- Convert integers from denary numbers to binary numbers or
hexadecimal numbers, or vice versa.
- Adopt two’s complement for
the representation of negative integers.
- Perform simple calculations (addition and subtraction only)
on binary numbers and analyse overflow errors.
- In understanding errors, minimum and maximum
numbers an n-bit can hold (maximum 2 bytes) should be considered.
- Know how characters are represented
by using common international standards such as American Standard Code for
Information Interchange (ASCII), the Big-5 code, the Guobiao (GB) code and the
Unicode.
- The relationship between the size
of the character set and the representation should be explained. Recall of specific codes is not required.
- Know briefly how different multimedia
elements are digitised. Convert them into different file formats and
compare them for storing the same data.
- Elementary file conversion is
required but not the editing of a file. Students should be given the experience in creating various file formats such
as wav vs. mp3, bmp vs. jpg, and avi vs. mpeg2.
Bits vs combinations
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No. of bits
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Possible combinations
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Calculation of combinations
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1 bit
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0,1
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21=2
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2 bits
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00,01,10,11
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22=4
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…
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…
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…
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n bits
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2n
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Representation of negative integers
Use 2’s complement method in modern computer
Suppose we use 4 bits to represent number: first bit is the
sign (+/-) and remaining bits are the size
For 0 and positive numbers, the sign bit is 0
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number
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In binary form
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number
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In binary form
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0
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0000
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4
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0100
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1
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0001
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5
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0101
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2
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0010
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6
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0110
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3
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0011
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7
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0111
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For negative numbers, we can derive the binary form from the
positive number using 2’s complement method
-1:
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steps
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Positive number
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0001
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1’s complement
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1à0,
0à1
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1110
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2’s complement
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+1
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1111
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number
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In binary form
|
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number
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In binary form
|
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-1
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1111
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-5
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1011
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-2
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1110
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-6
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1010
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-3
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1101
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-7
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1001
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-4
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1100
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-8
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1000
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So, the range of numbers represented by 4 bits is -23
to 23-1.
I.e. the range of numbers represented by n bits is -2n-1 to 2n-1-1
Overflow errors
- For 2 numbers with different signs, their sum will not
overflow.
- If the 2 numbers have same signs, overflow may happen. i.e.
when the result has different sign bit, overflow has occurred.
- e.g. 1111 + 1000 = (1)0111 = 0111 (overflow error)
Character representation
- ASCII (American Standard Code for Information Interchange),
7 bits for each character
- Big-5 code: Traditional Chinese, 2 bytes for each character
- GB (Guobiao) Code: Simplified Chinese, 2 bytes for each
character
- Unicode: Characters of different languages (If you need to
use traditional and simplified Chinese at the same time, use Unicode), 1 to 4
bytes for each character
Multimedia elements
File size depends on:
- Resolution: dots per inch
- Color depth: bits per pixel (determines the range of
possible colours)
- File formats:
- BMP: Bitmap. Uncompressed format à large file size
- JPEG: Joint Photographic Experts Group. Lossy compression à
small file size, commonly used in the internet and supported by most browsers
- GIF: Graphics Interchange Formats. Supports animation and
transparency. 256 colours only à
not good for photos
- PNG: Portable Network Graphics. Lossless compression à
file size bigger than JPEG. Support more colour than GIF à
better image quality than GIF
File size depends on:
- Bit depth/sample resolution: number of bits used in each
sample
- Sampling rate: number of samples per second (Hz)
- Duration
- File formats:
- Uncompressed format:
- WAV: WAVeform audio file. Useful for
further editing.
- Compressed format:
- MP3: MPEG-1 Audio Layer 3.
- WMA: Windows Media Audio.
File size affected by:
- Resolution ~image size
- Color depth: number of bits per pixel
- Frame rate – frame rate per second fps
- Duration
- File formats:
- Uncompressed: better video quality
- AVI: Audio Video Interleave
- Compressed: smaller file size
- MP4: MPEG layer 4: support streaming, store other data such as subtitles, scene
descriptions
- WMV: Windows Media Video
- Digitising multimedia elements
Reasons:
- Online access
- searching
- preservation of the originals
- allow further editing
- Compression of file/files
Reasons:
- Reduce file size – less storage space and faster
transmission in network
- Sending multiple files as one single file, file structure
maintained
- Encryption – security
Relevant past paper:
DSE ICT Paper 1B(SP-2017): PP 1c. 2012 3dii,4aii,5abii,iii.
2013 2a,3d. 2014 1b,4di. 2015 5di. 2016 1abc,5bi. 2017 1bc,2ai,b,4c.
References:
http://www.cwu.edu/~borisk/311/lecture/311-lec8.html
https://www.tutorialspoint.com/multimedia/multimedia_images_graphics.htm
https://isaaccomputerscience.org/concepts/gcse_data_sound?examBoard=all&stage=all&topic=gcse_data_representation
https://support.biamp.com/General/Video/Video_Basics
https://www.apowersoft.com/what-is-mp4-format.html
http://www.micrographics.co.nz/why-digitise/
https://officeorbiter.com/what-is-file-compression/
Learn more:
Example of audio header - https://www.codeproject.com/Articles/8295/MPEG-Audio-Frame-Header