Data Types: From Reality to the Computer

• rocks to paper numbers to short/long
• parts of rocks to money to decimals to float/double
• truth to bool

Common feature: values and operations.

  Type         Values                     Operations
--------------------------------------------------------------------------------------
   whole        -2billion..2billion        + - * / mod < > <= >= == =/=
                                           output input =
   decimal      e-308,e308  ~13 sig fig    + - * /     < > <= >= == =/=
                                           output input =
   logical      true,false                                       == =/=
                                           output input = AND OR NOT
   character    ASCII                                  < > <= >= == =/=
                                           output input =

More Complex Data

• Complex numbers

     Data:
        a + bi --+               ____
                 |- symbol for \/ -1   (character)
        a + bj --+
       /     \
     real   imaginary
     part    part
    (decimal)  (decimal)
  
     Operations:  + - * / == =/= input output =
                  conjugate magnitude
  

• Rational numbers

     Data:
        a  -- numerator    (whole)
       ---
        b  -- denominator  (whole)
  
     Operations:  + - * / < > <= >= == =/= input output =
                  reciprocal asdecimal simplify
  

Common feature: data and operation descriptions. Together these make the Abstract Data Type (ADT).

Nesting and ADTs: sub-data types

• A Point in a Circle
• A new look at the Brick

Collected Examples

• Complex
• Point & Circle
• Brick