Notes-for-CAIE

Table of contents

• 3.1.1 User-defined data types
  • Why user-defined types are necessary
  • Define composite data type
  • Define non-composite data type
• 3.1.2 File organisation and access
  • Benefits of using serial file organization
  • How to add record with random organization files
• 3.1.3 Real numbers and normalised floating-point representation
  • Overflow and underflow
  • Why 0.1+0.2 in floating-point representation is not precise
  • Effects of the number of bits on range and precision

3.1.1 User-defined data types

• show understanding of why user-defined types are necessary
• define and use non-composite types: enumerated, pointer
• define and use composite data types: set, record and class/object
• choose and design an appropriate user-defined data type for a given problem

Why user-defined types are necessary

w19 33 Q5 [2]

• No suitable data type is provided by the language used.
• The programmer needs to specify a new data type
• … that meets the requirements of the application.

Define composite data type

s18 33 Q2 [1]

• Data type constructed from other data types.

Define non-composite data type

s18 33 Q2 [1]

• Single data type that does not include a reference to another type.

3.1.2 File organisation and access

• show understanding of methods of file organisation: serial, sequential (using a key field) and random (using a record key)
• show understanding of methods of file access:
  • sequential access for serial and sequential files
  • direct access for sequential and random files
• select an appropriate method of file organisation and file access for a given problem

Benefits of using serial file organization

s15 31 Q3.b.ii [2]

• No need to re-sort data every time when new data is added
• Only a small file so search will require little processing
• New records can easily be applied

How to add record with random organization files

s15 33 Q4.b.ii [3]

1. StationID is hashed to produce home location
2. If home location is free, record inserted
3. Else overflow method used to find free location

3.1.3 Real numbers and normalised floating-point representation

• describe the format of binary floating-point real numbers
• convert binary floating-point real numbers into denary and vice versa
• normalise floating-point numbers
• show understanding of the reasons for normalisation
• show understanding of the effects of changing the allocation of bits to mantissa and exponent in a floating-point representation
• show understanding of how underflow and overflow can occur
• show understanding of the consequences of a binary representation only being an approximation to the real number it represents (in certain cases)
• show understanding that binary representations can give rise to rounding errors

Overflow and underflow

w19 33 Q1 [2]

• overflow: exponent becomes too large.
• underflow: number so small that cannot be represented.

Why 0.1+0.2 in floating-point representation is not precise

w15 32 Q1.c [3] w15 31 Q1.c [3]

Sample Questions: Why OUTPUT (0.1 + 0.2) gives 0.30000000000000001; Why 0.1 + 0.1 + 0.1 = 0.29999999

• 0.1 / 0.2 cannot be represented precisely in binary
• Adding approximate representations gives greater differences
• Summed differences significant enough to be seen

Effects of the number of bits on range and precision

s18 33 Q1 [2]

component	effect
mantissa	precision
exponent	range