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• Base


  The number of digits that a number system can use to represent numbers
• Place value


  Digits in certain positions have a specific value
• Number systems


  • Denary (Base 10)
  • Binary (Base 2)
• Bits (binary digits)


  0 and 1

  
• All data and characters are represented in binary

  
• Binary place values


  • 128
  • 64
  • 32
  • 16
  • 8
  • 4
  • 2
  • 1
• Denary prefixes


  • kilo- (k) x10^3
  • mega- (M) x10^6
  • giga- (G) x10^9
  • tera- (T) x10^12
• Binary prefixes


  • kibi- (Ki) x2^10
  • mebi- (Mi) x2^20
  • gebi- (Gi) x2^30
  • tebi- (Ti) x2^40
• Binary Coded Decimal (BCD)


  Binary representation where each positive denary digit is represented by a sequence of 4 bits (nibble)

  
• Two's complement


  Representing a negative number in binary by making the most significant bit (MSB) a sign bit, which indicates whether the number is positive or negative

  
• Converting negative denary to binary two's complement


  1. Find the binary equivalent of the denary number (ignoring the -ve sign)

  2. Add extra 0 bits before the MSB, to format binary number to 8 bits

  3. Convert binary number to one's complement (flip the bits)

  4. Convert binary number to two's complement (add 1)

  
• Converting binary two's complement to denary


  1. Flip all the bits

  2. Add 1

  3. Convert binary to denary and put a -ve sign
• Hexadecimal


  Base 16 number system with possible digits 0 to 9 and A to F
• Hexadecimal


  • A5 = (16x10) + (1x5) = 165

  65 = 65÷16=4 Remainder 1∴ = 41
• Character encoding standards


  • ASCII
  • Extended ASCII
  • Unicode
• ASCII


  Only English alphabets can be represented, each character takes up 7 bits
• Extended ASCII


  Also includes most European languages' alphabets, each character takes up 8 bits
• Unicode


  Superset for ASCII & extended ASCII, recognized by various global languages, each character takes up 2 or 4 bytes
• Bitmap images


  Data encoded by assigning a solid colour to each pixel through bit patterns
• Pixels


  Smallest picture element whose colour can be accurately represented by binary
• Bitmap file header


  Contains metadata contents of the bitmap file, including image size, number of colours, etc.
• Image resolution


  Pixel density measured by no. of pixels/cm
• Screen resolution


  Number of pixels which can be viewed horizontally & vertically on the device's screen
• Colour depth


  Number of bits used to represent the colour of a single pixel
• Colour depth increases


  Colour quality increases but file size increases
• Vector graphics


  Made up of drawing objects which are mathematically defined constructs
• Drawing list


  Set of commands defining the vector properties to draw lines & curves
• Vector graphics are scalable without losing quality unlike bitmaps
• Analogue data


  Continuous electrical signals

  
• Digital data


  Discrete electrical signals

  
• Sound signals


  Vibrations through a medium, hence analogue in nature
• Digitizing sound


  1. Sampling the sound wave's amplitude at set time intervals

  2. Encoding the samples as a binary number sequence

  
• Sampling rate


  Number of samples taken per unit time
• Sampling rate increases


  Accuracy of digitized sound wave representation increases but file size increases
• Sampling resolution


  Number of bits used to encode each sample

  
• Sampling resolution increases


  Accuracy of digitized sound wave increases but file size increases
• Bit rate


  Number of bits for storing 1 second of sound
• Lossless compression


  Allows original data to be perfectly reconstructed from compressed file
• Lossless compression


  • Bitmap (.bmp), vector graphic (.svg) and .png images, text file compression, database records
• Run-length encoding (RLE)


  Form of lossless compression that reduces file size of a sequence of elements which has adjacent, identical elements