Computer Science

• Every one of us is used to the decimal or denary (base 10) number system. This uses the digits 0 to 9 which are placed in 'weighted' columns.
• Designers of computer systems adopted the binary (base 2) number system since this allows only two values, 0 and 1. No matter how complex the system, the basic building block in all computers is the binary number system.
• Binary number system


  The binary system uses 1s and 0s only which gives these corresponding weightings: 128, 64, 32, 16, 8, 4, 2, 1
• Converting from binary to denary and from denary to binary

  1. Each time a 1 appears in a column, the column value is added to the total

  2. Placing 1s in the appropriate position so that the total equates to the denary number

  3. Successive division by 2; the remainders are then written from bottom to top to give the binary value
• One's complement


  Each digit in the binary number is inverted (0 becomes 1 and 1 becomes 0)
• Two's complement


  Each digit in the binary number is inverted and a '1' is added to the right-most bit
• The two's complement uses these weightings for an 8-bit number representation: -128, 64, 32, 16, 8, 4, 2, 1
• Two's complement


  Method used to represent negative numbers in binary
• Converting denary to binary using two's complement

  1. Invert the digits

  2. Add 1
• Converting denary to binary using two's complement

  • +104 becomes 1 0 0 1 1 0 0 0
  • -104 becomes 1 0 0 1 1 0 0 0
• Two's complement makes binary addition and subtraction more straightforward
• The byte is the smallest unit of memory in a computer
• Memory size units


  • Kilobyte (KB)
  • Megabyte (MB)
  • Gigabyte (GB)
  • Terabyte (TB)
  • Petabyte (PB)
• SI (base 10) system of units


  1 kilo = 1000
• IEC (binary) system of units

  • 1 kibibyte (KiB) = 1024
  • 1 mebibyte (MiB) = 1,048,576
  • 1 gibibyte (GiB) = 1,073,741,824
• Internal memories should be measured using the IEC system
• Hexadecimal


  Base 16 number system using digits 0-9 and A-F
• Converting binary to hexadecimal

  1. Split binary into groups of 4 bits

  2. Convert each group to equivalent hexadecimal digit
• Converting hexadecimal to binary


  Take each hexadecimal digit and write the 4-bit binary code
• Converting binary to hexadecimal

  • 1 0 1 1 1 1 1 0 0 0 0 1 becomes B E 1

  1 0 0 0 0 1 1 1 1 1 1 1 0 1 becomes 2 1 F D
• Converting hexadecimal to binary

  • 4 becomes 0 1 0 0

  F becomes 1 1 1 1

  0 8 becomes 0 0 0 0 1 0 0 0
• Memory dump


  Output of a computer's memory contents, often in hexadecimal

  
• Binary-coded decimal (BCD)


  1. bit code to represent each decimal digit
• BCD representation


  • 0 0 0 0 = 0

  0 1 0 1 = 5

  1 0 0 1 = 9
• Uses of BCD


  Representation of digits on calculator/clock displays

  Storing monetary values accurately
• ASCII code
• Binary addition


  1. 0 + 0 = 0

  2. 0 + 1 = 1

  3. 1 + 0 = 1

  4. 1 + 1 = 1 0 (carry 1)
• This produces 1 1 0 1 which isn't a denary digit; this will flag an error and the computer again needs to add 0 1 1 0
• Adding 1 to 0 0 0 0 0 0 0 0


  Produces 0 0 0 0 0 0 0 1
• Final answer: 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 which is 1.31 in denary – the correct answer
• ASCII code


  American Standard Code for Information Interchange, set up in 1963 for use in communication systems and computer systems
• The standard ASCII code character set consists of 7-bit codes (0 to 127 denary or 0 to 7F in hexadecimal)
• The ASCII code table includes 32 control codes (which use up codes 0 to 31 (denary) or 0 to 19 (hexadecimal))
• Extended ASCII uses 8-bit codes (128 to 255 in denary or 80 to FF in hex)
• Unicode


  Allows characters in a code form to represent all languages of the world, thus supporting many operating systems, search engines and internet browsers used globally
• Unicode can support several thousand different characters in total
• Goals of the Unicode consortium

  • Create a universal standard that covered all languages and all writing systems
  • Produce a more efficient coding system than ASCII
  • Adopt uniform encoding where each character is encoded as 16-bit or 32-bit code
  • Create unambiguous encoding where each 16-bit or 32-bit value always represents the same character
  • Reserve part of the code for private use to enable a user to assign codes for their own characters and symbols
• Vector graphics


  Images that use 2D points to describe lines and curves and their properties that are grouped to form geometric shapes
• Creating vector graphics


  1. Using computer aided design (CAD) software

  2. Using an application with a drawing canvas on the screen
• Vector graphic


  • Contains a drawing list (in file header) with the command for each object, the attributes that define the properties of each object, and the relative position of each object
  • Dimensions of each object are not defined, but the relative positions of objects to each other in the final graphic need to be defined
  • Scaling up the vector graphic image will result in no loss of quality