4.5 Data Representation

4.5 Data Representation

1. Number Systems

   • 4.5.1 Number Systems
   • natural numbers
   • Integer numbers
   • Rational numbers
   • Irrational numbers
   • Real numbers
   • Ordinal numbers
   • Counting vs. measurement

2. Number bases

   • 4.5.2 Number bases
   • decimal, binary, hexadecimal
   • Base Conversions

3. Units of information

   • 4.5.3 Units of information
   • Bits vs. Bytes
   • Decimal vs. Binary prefix

4. Binary number system

   • 4.5.4 Binary Number system
   • Signed vs. Unsigned binary
   • Unsigned binary arithmetic
     • Addition
     • Multiplication
   • Signed binary using 2's complement
     • +ve and -ve integer representation
     • Substraction
     • Range
   • Fixed point binary
   • Floating point binary
   • Rounding errors
   • Absolute vs. Relative errors
   • Range & Precision
   • Normalisation of floating point numbers
   • Underflow vs. Overflow

5. Information coding systems

   • 4.5.5 Information coding systems
   • Character code vs. pure binary representation
   • ASCII vs. Unicode
   • Error checking & correction
     • Parity bits
     • Majority voting
     • checksums
     • check digits

6. Bit patterns, images and sound representation

   • 4.5.6 Bit patterns, images and sound representation
   • Analogue vs. Digital data
   • Analogue vs. Digital signal
   • Analogue/ Digital conversion
   • Sound representation
     • Sampling resolution
     • Sampling rate
     • Nyquist theorem
     • Sample size calculation
     • MIDI
     • Data compression
       • RLE
       • Dictionary based method
       • lossless vs. lossy
   • Graphics representation
     • Bitmapped graphics
       • Resolution
       • Colour depth
       • Size
     • Vector graphics
     • Bitmapped vs. Vector graphics

7. Encryption

   • 4.5.7 Encryption
   • cipher
   • plaintext
   • cipher text
   • Caesar cipher
     • Encrypt
     • Decrypt
   • Vernam cipher
     • Encrypt
     • Decrypt
   • Computational security
   • Perfect security