2.4 Arithmetic and Logical Operators

Python provides a wide range of operators that allow you to perform various operations on data, including arithmetic calculations and logical comparisons. Understanding how these operators work is essential for performing mathematical computations and making decisions in your code.

In this section, we will explore:

1. Arithmetic Operators
2. Logical Operators
3. Operator Precedence
4. Short-Circuiting in Logical Operators

2.4.1 Arithmetic Operators

Arithmetic operators are used to perform mathematical operations on numeric data types (integers and floats). The common arithmetic operations include addition, subtraction, multiplication, division, and more.

Here is a list of Python's arithmetic operators:

Examples of Arithmetic Operations

1. Division and Floor Division

Exponentiation
The exponentiation operator (**) raises the first number to the power of the second number.

x = 2
y = 3
print(x ** y)  # Output: 8 (2^3)

Modulus (Remainder)
The modulus operator (%) returns the remainder when dividing two numbers.

x = 10
y = 3
print(x % y)  # Output: 1

Floor Division (//) returns the largest integer less than or equal to the result (also known as integer division).

x = 10
y = 3
print(x // y)  # Output: 3

Division (/) returns a float, even if the result is a whole number.

x = 10
y = 2
print(x / y)  # Output: 5.0

Multiplication

x = 5
y = 4
print(x * y)  # Output: 20

Addition and Subtraction

x = 10
y = 3
print(x + y)  # Output: 13
print(x - y)  # Output: 7

2.4.2 Logical Operators

Logical operators are used to perform logical operations (also called boolean operations) on Boolean values (True or False). These operators help control the flow of the program by allowing you to perform comparisons and combine conditions.

Here is a list of Python's logical operators:

Examples of Logical Operations

• The and operator returns True only if both conditions are True. Otherwise, it returns False.
• The or operator returns True if at least one of the conditions is True. It returns False only if both conditions are False.
• The not operator inverts the boolean value. If the expression is True, it becomes False, and vice versa.

not Operator

x = True
print(not x)  # Output: False

or Operator

x = 5
print(x > 3 or x > 10)  # Output: True (one condition is True)
print(x < 3 or x > 10)  # Output: False (both conditions are False)

and Operator

x = 5
print(x > 3 and x < 10)  # Output: True (both conditions are True)
print(x > 3 and x > 10)  # Output: False (one condition is False)

Combining Logical Operators

Logical operators can be combined to create complex conditions.

Example:

x = 7
print((x > 5 and x < 10) or (x == 0))  # Output: True

2.4.3 Relational (Comparison) Operators

Relational (comparison) operators are used to compare two values and return True or False depending on the result. These operators are commonly used in conjunction with logical operators for decision-making in your code.

Here is a list of Python's relational operators:

Examples of Relational Operators

Greater than or Equal to and Less than or Equal to

x = 5
print(x >= 5)   # Output: True
print(x <= 4)   # Output: False

Greater than and Less than

x = 15
print(x > 10)   # Output: True
print(x < 20)   # Output: True

Equality and Inequality

x = 10
y = 20
print(x == y)  # Output: False
print(x != y)  # Output: True

2.4.4 Operator Precedence

When multiple operators are used in an expression, operator precedence determines the order in which the operations are evaluated. Python follows a specific precedence rule to resolve this.

From highest to lowest precedence:

1. Parentheses: ()
2. Exponentiation: **
3. Unary operators: +, -, not
4. Multiplication, Division, Modulus, and Floor Division: *, /, %, //
5. Addition and Subtraction: +, -
6. Relational operators: >, <, >=, <=
7. Equality operators: ==, !=
8. Logical and
9. Logical or

Examples of Operator Precedence

Example 1:

x = 5 + 2 * 3  # Multiplication has higher precedence than addition
print(x)  # Output: 11

Example 2:

x = (5 + 2) * 3  # Parentheses change the order of evaluation
print(x)  # Output: 21

2.4.5 Short-Circuiting in Logical Operators

Python uses short-circuit evaluation for logical operators and and or. This means that Python stops evaluating an expression as soon as the result is determined.

and Short-Circuiting

In the case of and, if the first condition is False, Python does not evaluate the second condition because the entire expression can never be True.

Example:

x = 5
print(x > 10 and x < 20)  # Output: False (Python doesn't check the second condition)

or Short-Circuiting

For or, if the first condition is True, Python does not evaluate the second condition because the entire expression will be True regardless of the second condition.

Example:

x = 5
print(x > 3 or x > 10)  #

 Output: True (Python doesn't check the second condition)

2.4.6 Summary

• Arithmetic operators allow you to perform basic mathematical operations such as addition, subtraction, multiplication, division, and more.
• Logical operators help you combine multiple conditions, using and, or, and not to control the flow of your program.
• Relational operators are used to compare values and return a boolean (True or False).
• Operator precedence determines the order in which operations are performed in an expression.
• Short-circuiting allows Python to skip unnecessary evaluations in logical expressions for efficiency.

Understanding how to use these operators effectively is key to performing calculations, making decisions, and controlling the logic of your Python programs.