Data Representation

Units

• bit, byte, kilobytes, megabytes, gigabytes, terabytes, petabytes
• 1000 base, MB
• 1024 base, MiB
• b vs B

Numerical

Encoding

• Excess 3
• BCD
• Exercise: base 10, 9’s complement vs 10’s complement

Integers(fixed point)

• 2’s complement: mainly used
• 1’s complement: postive & negative 0
• Sign and magnitude
• Gray code
  • Benefit: filp 1 bit at a time, has a good pattern

Floating point

• Sign and magnitude
• Float(32bits, 1 + 8 + 23), excess-127
• Double(64bits, 1 + 11 + 48)

Overflow & Underflow

Conversion

• 10110.0011~(2)~
• 1101~(2)~
  • unsigned
  • signed
• float: 1 01111111 00000 00000 00000 00000 001 = -(1+2^-23^)

Text

• ASCII
• Unicode
  • Implementation

Audio

1. Sampling
   • Sample rate(e.g. 44100Hz)
   • Duration(e.g. 3s)
2. Quantization
   • Bit per sample(bit depth, e.g. 24 bit)
3. Encoding
   • Lossy: mp3, ape…
   • Lossless: wav, flac…

• Bit rate = sample rate * bit depth (e.g. 1033kbps)

Images

• Raster(bitmap) graphics: bmp, jpeg, gif…
• Vector graphics: svg…
• Resolution
• Color depth
  • True color: 24 bits, 3 channels
  • Indexed color: a subset color of true color

Videos

• Mpeg4, avi, mkv…

Questions

1. Convert the 1010.01011~(2)~ to decimal and octal.
2. Convert the 734.2371~(8)~ to decimal and binary.
3. Convert the 31.96~(10)~ to octal and binary.
4. Represent 31.96~(10)~ with single precision floating point.
5. When will overflow and underflow happen?
6. Give 1 example of overflowing and 1 example of underflowing.
7. If a piece of audio has 500 bytes, duration of 5s, bit depth is 10bit. What’s its bit rate and sampling rate?
8. How do resolution and color depth affect an image?