representing numbers

• Contents of this TOPIC

  • Representation of numbers
  • Storage of characters
  • Representation of graphics and sound
• Denary


  Base 10 or decimal counting system
• Binary


  Base 2: computer systems can only store and process Binary digITs, also known as BITs. A BIT is either a 1 or 0.
• Hexadecimal


  Base 16: 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. The hexadecimal system is widely used as binary numbers can be quickly converted into hexadecimal numbers that are more convenient for humans to use.

  
• Arithmetic shift functions


  1. Shifting the position of the bits stored is very fast and much faster than the actual arithmetic operation for a computer

  2. Left shift (multiplying): e.g. 0011002 (1210) shifted one place left gives 0110002 (2410), equivalent to multiplying by 2

  3. Right shift (dividing): e.g. 0011002 (1210) shifted one place right gives 0001102 (610), equivalent to dividing by 2
• Binary addition


  1. 0 + 0 = 0

  2. 1 + 0 = 1

  3. 0 + 1 = 1

  4. 1 + 1 = 0 (carry 1 to next column)

  5. 1 + 1 (and carrying from last column) = 1 (carry 1 to next column)
• Overflow


  If the result of an addition or shift process results in a binary number that is too large to fit in the space available then an overflow has occurred. The CPU detects the carry and sets the overflow flag to true.
• Characters are typically represented using binary code. The most common encoding scheme is ASCII.
• ASCII


  A basic character encoding standard using 7 or 8 bits to represent 128 or 256 characters, mainly covering English letters, numerals, and symbols.
• Unicode


  A modern character encoding standard using 16 bits or more for a broader character set, supporting characters from various languages.
• Common data types


  • Integer
  • Real (float)
  • Boolean
  • Character
  • String
• Integer


  Stores whole numbers, can be positive or negative
• Real (float)


  Stores decimal numbers
• Boolean


  Can only store one of two values - yes/no, true/false, 0/1
• Character


  Stores a single character - can be text, number or symbol
• String


  Can store any sequence of alphanumeric characters including text, numbers and symbols
• Integers are used for storage space and processing speed reasons