Transform representations: dates, fractional marks and money

The way a value is displayed need not be the way it is stored. A useful representation makes the required comparisons and calculations easier, while a display operation converts it back to human-readable form.

Represent a date as its day index #

The lecture uses 1 January = 0, 2 January = 1, 31 January = 30 and 1 February = 31. For a fixed non-leap year, valid day indices run 0–364. In a leap year they run 0–365. You need a consistent year/calendar convention, especially for 29 February and dates after February.

With that convention, compare dates by comparing their integer indices. Convert the index to a date string for display: print(31) produces “1 Feb”. Adding a number of days to a date or taking a difference between dates can be meaningful with boundary rules; adding two calendar dates is not automatically meaningful just because both are stored as integers.

Keep two decimal places by scaling #

If marks have at most two decimal places, multiply by 100 and store integer hundredths. 62.5 becomes 6250, and 75.25 becomes 7525. To display, divide the scale back out. Single-subject marks 0–100 therefore need stored integers 0–10000, as corrected in the supplied slides.

Preserve the scale during operations #

Add or compare values only after confirming compatible scales and units. Stored marks 6250+7525 = 13775 represent 137.75 total marks; that result requires a total type wider than single-subject Marks. Stored amounts Rs 27.50 and Rs 12.25 add as 2750+1225 = 3975 paise, displayed Rs 39.75.

If both quantity and price are scaled by 100, multiplying their stored integers creates a scale of 10,000. For 1.25 kg at Rs 20.00 per kg, 125×2000 = 250000 hundredths-of-hundredths. Divide by 100 to obtain 2500 paise, displayed Rs 25.00. State the rescaling and any rounding rule. Do not interpret 250000 as paise directly.

Why not drop the fractional part? #

Turning 62.5 into 62 or 63 loses information and can affect comparisons. A floating-point type is another option, but it has finite precision; it does not store arbitrary real numbers exactly. The lesson’s fixed-scale representation is especially simple when the allowed decimal precision is known.

Source: Lecture 1.9 — Transformation of sub-datatypes. Small teaching datasets and diagrams are prepared for these notes; lecture and tutorial totals are identified explicitly.