Operators in Depth

Operators are the verbs of the programming world. They take data (operands) and perform actions on them to produce new values. While basic math is straightforward, Python’s operators have unique behaviors—like floor division and short-circuit logic—that are essential for writing robust code.

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1. Arithmetic Operators

Python handles math with high precision, but you must understand the difference between the two types of division.

Symbol	Operation	Behavior	Example
+	Addition	Sums values.	5 + 2 = 7
-	Subtraction	Finds difference.	5 - 2 = 3
*	Multiplication	Finds product.	5 * 2 = 10
/	True Division	Always returns a float.	5 / 2 = 2.5
//	Floor Division	Returns the integer part (rounds down).	5 // 2 = 2
%	Modulus	Returns the remainder.	5 % 2 = 1
**	Exponentiation	Power of (x to the y).	5 ** 2 = 25

Floor Division with Negatives

A common pitfall is assuming // just “chops off” the decimal. It actually rounds down towards negative infinity.

print(-7 // 2) # Output: -4 (not -3!)

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2. Comparison & Chaining

Comparison operators evaluate the relationship between two values and return a bool.

Operator	Meaning
==	Equal value
!=	Not equal
> / <	Greater / Less than
>= / <=	Greater / Less or equal

Chained Comparisons

Python allows you to write mathematical ranges just like you would on paper. This is more readable than using and.

chaining.py

age = 25
# Standard way: if age >= 18 and age <= 65:
# Pythonic way:
if 18 <= age <= 65:
    print("Working age adult")

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3. Logical Operators & Short-Circuiting

and, or, and not allow you to build complex decision trees.

Short-Circuit Evaluation (Deep Dive)

Python is efficient. It stops evaluating an expression as soon as the result is certain.

1. A and B: If A is False, Python returns A and does not even look at B.
2. A or B: If A is True, Python returns A and does not even look at B.

short_circuit_logic.py

def log_and_return():
    print("This ran!")
    return True

# Since the first part is False, the function NEVER runs.
result = False and log_and_return()

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4. Bitwise Operators (Under the Hood)

Bitwise operators treat integers as strings of binary 0s and 1s. These are primarily used in low-level systems programming, cryptography, and performance optimization.

Operator	Name	Action	Example (5 is 0101, 3 is 0011)
&	AND	1 if both bits are 1.	5 & 3 -> 0001 (1)
`	`	OR	1 if either bit is 1.
^	XOR	1 if bits are different.	5 ^ 3 -> 0110 (6)
~	NOT	Inverts all bits.	~5 -> -6 (due to 2’s complement)
<<	L-Shift	Moves bits left (multiplies by 2).	5 << 1 -> 1010 (10)
>>	R-Shift	Moves bits right (divides by 2).	5 >> 1 -> 0010 (2)

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5. Operator Precedence

When you mix operators, Python follows a strict hierarchy (order of operations).

1. Parentheses () (Always use these to be explicit!)
2. Exponentiation **
3. Multiplication/Division *, /, //, %
4. Addition/Subtraction +, -
5. Comparisons ==, >, <, etc.
6. Logical not
7. Logical and
8. Logical or

# Is it (10 + 2) * 5 or 10 + (2 * 5)?
result = 10 + 2 * 5
# Multiplication is higher: 10 + 10 = 20

Best Practice

Even if you know the precedence rules, use parentheses to make your intent clear to other developers. (10 + 2) * 5 is much safer than relying on memory.