Notes on Data Types and Subtypes

Introduction to Subtypes

• Creating subtypes can be complex and requires careful design.

Date as a Subtype

• Definition of Date: Represented as a string (e.g., "4th June", "31st January").
  • Limitations of String Representation:
    • Cannot perform comparisons (e.g., less than, greater than).
    • Cannot perform arithmetic operations (e.g., adding days).

Proposed Solution for Date Representation

• Convert date into an integer representing the day of the year.

  • Example:
    • January 1 = 0
    • January 31 = 30
    • February 1 = 31
    • Last day of a normal year = 364
    • Last day of a leap year = 365

• Benefits:

  • Allows for integer operations like addition, subtraction, and comparisons.
  • Enables printing in a conventional format (e.g., converting integers back to date strings).

Operations on Dates

• Define operations like:
  • print(int) to convert integer back to string (date).
  • Addition, subtraction, and comparison of dates.

Fractional Marks as a Subtype

• Issue with Fractional Marks:
  • Example: Marks like 62.5 should be stored accurately without losing information.
  • Storing as integers can lead to loss of precision (rounding errors).

Proposed Solution for Marks Representation

• Use float data type to represent real numbers.
  • Allows for complex real numbers and large/small values.
• Alternative Solution:
  • Multiply fractional marks by 100 (to convert to integer).
  • Example: 62.5 becomes 6250.

Operations on Marks

• Define operations:
  • print(int) to convert back to fractional format.
  • Allow addition, subtraction, and comparison of marks.

Handling Amounts and Prices

• Example of Price Representation:
  • Prices often have two decimal places (e.g., 27.50).
• Convert to integer by multiplying by 100 (2750).
• Operations:
  • Addition, subtraction, and comparison of amounts.
  • Print function to display the value in currency format.

Handling Quantity

• Quantities can be:
  • Whole numbers (e.g., 3 cans).
  • Fractional quantities (e.g., 1.25 kilos).
• Multiply fractional quantities by 100 to store as an integer (e.g., 1.25 becomes 125).
• Operations:
  • Addition, subtraction, and comparison of quantities.
  • Print function to display the value in correct format.

Conclusion

• Designing subtypes for data types like dates, marks, amounts, and quantities is essential for efficient data handling and operations.