Data Representation (A Level)

• User-defined types model the problem: non-composite (enumerated, pointer) and composite (record, set, class).
• Serial files store records in the order they arrive; sequential files keep them in key order; random files place each record at an address calculated from its key.
• Sequential access reads from the start; direct access goes straight to a record (sequential files with an index, random files by hashing).
• A hashing algorithm turns a key into an address. Collisions are handled by storing in the next free slot or in an overflow area.
• Floating point = mantissa × 2^exponent, both in two's complement. A normalised positive mantissa starts 0.1; a negative one starts 1.0.
• More mantissa bits give more precision; more exponent bits give more range.
• Overflow: a result too large for the exponent. Underflow: a result too close to zero. Many fractions such as 0.1 can only be approximated, which causes rounding errors.

Enumerated, pointer, set, record, class

A user-defined data type is one the programmer defines from the built-in types. They are needed because built-in types cannot model every problem: a type can restrict values to a sensible list, group related data under one name, or describe how data links together. This makes programs easier to read and harder to misuse.

Non-composite types (defined without reference to another type's structure)

TYPE Season = (Spring, Summer, Autumn, Winter)   // enumerated
TYPE TIntPointer = ^INTEGER                      // pointer to an INTEGER

DECLARE ThisSeason : Season
DECLARE MyPointer : TIntPointer
DECLARE Number : INTEGER
ThisSeason ← Summer
MyPointer ← ^Number          // MyPointer holds the address of Number
MyPointer^ ← 42              // stores 42 in Number (dereferencing)

An enumerated type lists every value the variable may take; the values are ordered, so Autumn > Summer is TRUE. A pointer type holds a memory address of data of the stated type; ^Number gives the address and MyPointer^ reads or writes the value at that address.

Composite types (built from other types)

TYPE Book                              // record
   DECLARE ISBN : STRING
   DECLARE Title : STRING
   DECLARE Price : REAL
   DECLARE OnLoan : BOOLEAN
ENDTYPE

TYPE LetterSet = SET OF CHAR           // set
DEFINE Vowels ('A', 'E', 'I', 'O', 'U') : LetterSet

DECLARE Library : ARRAY[1:500] OF Book
Library[1].Title ← "Hard Times"

A record groups fields of different types about one thing. A set holds an unordered collection of distinct values and supports operations such as membership, union and intersection. A class (see chapter 20) groups data and the methods that act on it; an object is an instance of a class.