Data Representation

• Logic


  Take binary information and give an output based on the Boolean operations
• Boolean operations


  • AND
  • OR
  • NOT
• Logic gates


  Special circuits built into computer chips that receive binary data, apply operations, then output a binary result
• NOT gate


  Takes a single input and gives a single output, where the output is always the opposite value to the input
• NOT gate


  • If input is 1, output is 0
  • If input is 0, output is 1
• AND gate


  Takes two inputs and gives one output, where the output is 1 only if both inputs are 1
• AND gate


  • If both inputs are 1, output is 1
  • Otherwise, output is 0
• OR gate


  Takes two inputs and gives one output, where the output is 1 if one or more inputs are 1
• OR gate


  • If one or more inputs are 1, output is 1
  • Otherwise, output is 0
• XOR gate


  Takes two inputs and gives one output, where the output is 1 if exactly one input is 1
• XOR gate


  • If exactly one input is 1, output is 1
  • Otherwise, output is 0
• Boolean operator symbols


  • NOT A
  • A AND B
  • A OR B
  • A XOR B
• Bit


  A single binary digit (1 or 0)
• Nibble


  4 bits
• Byte


  8 bits, enough to store one character
• Kilobyte (KB)


  1000 bytes
• Megabyte (MB)


  1000 kilobytes
• Gigabyte (GB)


  1000 megabytes
• Terabyte (TB)


  1000 gigabytes
• Binary number system


  Only uses the digits 0 and 1, with place values increasing by powers of 2 from right to left
• Binary place values


  • 128
  • 64
  • 32
  • 16
  • 8
  • 4
  • 2
  • 1
• Binary shift


  • Moves every bit in a binary number left or right a certain number of places
  • Left shifts multiply by 2 for each place
  • Right shifts divide by 2 for each place
• Hexadecimal (hex)


  • Another number system that uses 16 different digits (0-9, A-F)
  • Each hex digit represents a 4-bit binary number (a nibble)
• Programmers prefer hex over binary as it's shorter and easier to convert between
• ASCII


  1. bit character set used to represent characters in the English language, can represent 128 different characters
• Unicode


  Character set that covers all major languages, even those that use a completely different alphabet like Greek, Russian and Chinese
• You don't need to remember the ASCII codes for any specific characters, but if you're given the ASCII code of one character you should be able to work out the ASCII code for another character
• Bitmap images


  • Made up of lots of tiny dots called pixels
  • Colour of each pixel represented by a binary code
  • Number of colours related to number of bits in code
• Colour depth


  Number of bits used for each pixel
• Image size


  Number of pixels in the image, given as width x height
• Calculating file size of an image

  File size (in bits) = image size x colour depth (width x height x colour depth)
• There is also another type of image called a vector image, which is made of simple shapes and blocks of colour
• Analogue sound


  • Pieces of acoustically changing data
  • Needs to be converted to digital data so computers can read and store it
• Sampling


  Process of converting analogue to digital sound
• Digital sound


  • Represented by blocks of data that match the shape of the analogue signal
  • Quality can be improved by increasing sample rate and sample resolution
• Sample rate


  How many samples are taken per second, measured in Hz or kHz
• Sample resolution


  Number of bits available for each sample
• Calculating size of sound file

  File size (in bits) = sample rate (in Hz) x sample resolution x length (in seconds)
• Increasing sample rate or sample resolution will increase the file size
• Data compression


  Making file sizes smaller while trying to make the compressed file as true to the original as possible