number types

• natural numbers

  ℕ = { 0, 1, 2, 3, ... }

  
  

  natural numbers are positive, whole numbers that can be used for counting objects

  
  

  eg 5 fish
• integers

  ℤ = { ..., -1, 0, 1, ... }

  
  

  integers are positive or negative and whole numbers
• rational numbers

  ℚ = { 2/3, 0.8, 6, 7/4, etc}

  
  

  rational numbers can be expressed as exact fractions or ratios

  (includes d ecimals, f ractions and i ntegers)
• irrational numbers

  numbers that cannot be expressed as exact fraction

  (they have no end so have to be rounded at a degree of accuracy)

  eg pie, or √2
• irrational numbers

  numbers that cannot be expressed as exact fraction

  (they have no end so have to be rounded at a degree of accuracy)

  eg pie, or √2
• real numbers

  ℝ = { ... ,-1, 0, 1, √2, ... }

  
  

  includes rational and irrational numbers and are numbers used in measurement

  
  

  ( a set of all real world quantities )
• ordinal numbers

  used to describe the numerical position of an object in an ordered

  list

  
  

  eg for set = {'a', 'b', 'c' ...}

  
  

  'a' = 1st , 'b' = 2nd, 'c' = 3rd
• number systems

  includes decimal, binary and hexadecimal (hex)

  
  

  they are referred to by their base (number in subscript) which is the number of symbols used to construct values

  
  

  decimal for example is base 10 as it uses the symbols 0 - 9 to construct any number.

  
  

  11[base 10] and 11[base 2] would represent different values

  (11 and 3 respectively)
• hexadecimal

  base 16 , uses 0 - 9 and A - F (to represent 10 - 15)

  
  

  used because:

  • it is easier to read and remember by humans
  • quicker to write with less chance of error than binary
  • commonly used in colours and MAC addresses
  • easy to convert to and from binary

  (decimal is easy for humans to understand but not electronics, and binary is good for circuits but hard for humans)
• conversions

  hex to decimal

  3F5 -> (16^2 * 3) + (16 * 15) + (1 * 5 ) = 1013

  
  

  decimal to hex

  43 - > 43/16 = (2 r 11), 11 = B so 43 = 2B

  
  

  binary to hex

  11011000 -> 1101 = 13(D) , 1000 = 8 so 10111000 = D8