Programming Fundamentals

This section explores programming fundamentals for computer science, topics covered include: variables and constants, the three basic programming constructs, count-controlled iteration, condition-controlled iteration, nesting, operators and applying computer aided mathematics.

Variables and Constants

Variables and constants are used to store data values in a program. They are essential for creating flexible and reusable code.

Variables

A variable is a named storage location in memory where data can be held and manipulated.

Declaration and Assignment:

• Declaration: Specifying the name and type of the variable.
• Assignment: Giving the variable a value.

Example:

python

age = 16  # Declaration and assignment in Python

Properties of Variables:

• They can change value during program execution.
• Their names should be descriptive for clarity.

Constants

A constant is similar to a variable, but its value cannot change once assigned.

Advantages of Constants:

• They improve code readability by clearly indicating values that remain unchanged.
• They reduce the chance of errors caused by accidental changes.

Example:

Python
PI = 3.14159 # PI is a constant in this example

Global and Local Variables

Global Variables:

• Declared outside of functions and accessible throughout the program.
• Disadvantage: May lead to unexpected behaviour if modified in different parts of the program.

Local Variables:

• Declared within a function or block and accessible only there.
• Advantage: Reduces interference with other parts of the program.

The Three Basic Programming Constructs

All programs are built using three fundamental constructs: sequence, selection, and iteration.

Sequence

• The simplest construct.
• Instructions are executed in order, one after the other.

Example:

python

print("Hello")

print("World")

Selection

• Allows decisions to be made using conditions (if statements).
• The program follows different paths depending on whether the condition is true or false.

Example:

Python
 

if age >= 18:

   print("You are an adult.")

else:

   print("You are a minor.")

Iteration

• Involves repeating a block of code.
• Two main types of iteration: count-controlled and condition-controlled.

Count-Controlled Iteration

Count-controlled loops repeat a set number of times, typically using a for loop.

Example:

python

for i in range(5):  # Repeats 5 times

    print(i)
 

Condition-Controlled Iteration

Condition-controlled loops repeat until a condition is met. These can be implemented using while or repeat loops.

While Condition-Controlled Loops

Repeats as long as the condition is true.

Example:

python

counter = 0

while counter < 5:

   print(counter)

    counter += 1

Repeat Condition-Controlled Loops

Repeats at least once and then checks the condition (common in some languages but not in Python).

Pseudocode Example:

java

REPEAT

    counter = counter + 1

UNTIL counter >= 5

Infinite Loops

• A loop that never ends because the exit condition is never met.
• Usually an error but sometimes intentional, such as in servers.

Nesting

Nesting involves placing one construct inside another.

Nested Selection

Using an if statement inside another if statement.

Example:

python

if age > 12:

    if age < 20:

       print("You are a teenager.")

Nested Iteration

• A loop inside another loop.
• Common in tasks like matrix processing.

Example:

python

for i in range(3):

    for j in range(3):

       print(i, j)

Operators

Operators are symbols or keywords used to perform operations on data.

Mathematical Operators

• + (Addition)
• - (Subtraction)
• * (Multiplication)
• / (Division)
• // (Integer division)
• % (Modulus - remainder of division)
• ** (Exponentiation)

Comparison Operators

• == (Equal to)
• != (Not equal to)
• < (Less than)
• > (Greater than)
• <= (Less than or equal to)
• >= (Greater than or equal to)

Logical Operators

• AND (True if both conditions are true)
• OR (True if at least one condition is true)
• NOT (Reverses the truth value)

Applying Computer-Related Mathematics

Modulus

Returns the remainder of a division operation.

Example:

python

10 % 3  # Result: 1

Integer Division

Returns the whole number part of a division.

Example:

python

10 // 3  # Result: 3

Exponentiation

Raises a number to a power.

Example:

python

2 ** 3  # Result: 8

Use of Brackets

• Brackets determine the order of operations.
• Operations within brackets are evaluated first.

Example:

python

result = (3 + 2) * 4  # Result: 20
 

Summary of Key Concepts

Variables and Constants: Store data values with variables being changeable and constants fixed.

Programming Constructs: Sequence, selection, and iteration are the building blocks of programming.

Operators: Include mathematical, comparison, and logical operators for calculations and decision-making.

Mathematics in Programming: Concepts like modulus, integer division, and exponentiation are critical for many algorithms.

These concepts provide the foundation for creating effective and efficient programs.