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Python Interview Cookbook

Bitwise Operators

Bitwise Operators

The fundamental operators for manipulating individual bits.

Introduction

Python supports standard bitwise operators that operate on numbers bit by bit. These operations execute incredibly fast at the hardware level.

The Operators

Operator	Name	Symbol	Description	Example (A=5, B=3)
AND	`&`	`A & B`	Returns 1 if both bits are 1.	`101 & 011 = 001 (1)`
OR	`\\|`	`A \\| B`	Returns 1 if either bit is 1.	`101 \\| 011 = 111 (7)`
XOR	`^`	`A ^ B`	Returns 1 if the bits are different.	`101 ^ 011 = 110 (6)`
NOT	`~`	`~A`	Inverts all bits (flips 0 to 1 and 1 to 0).	`~101 = ...111010 (-6)`
Left Shift	`<<`	`A << 1`	Shifts bits left by \(N\) places (multiplies by \(2^N\)).	`101 << 1 = 1010 (10)`
Right Shift	`>>`	`A >> 1`	Shifts bits right by \(N\) places (integer divides by \(2^N\)).	`101 >> 1 = 010 (2)`

Operator Breakdown

AND (`&`)

Used to extract or check specific bits (masking).

# Check if a number is odd or even
# The last bit of an odd number is always 1, and even is 0.
x = 5 # 101
print(x & 1) # 1 (Odd)

y = 4 # 100
print(y & 1) # 0 (Even)

OR (`|`)

Used to set specific bits to 1.

# Set the lowest bit to 1 (making an even number odd, leaving odd unchanged)
x = 4 # 100
print(x | 1) # 101 (5)

XOR (`^`)

Exclusive OR. Extremely powerful for toggle operations and finding missing elements.

# XORing a number with itself always results in 0.
print(5 ^ 5) # 0

# XORing a number with 0 leaves the number unchanged.
print(5 ^ 0) # 5

Shift Operators (`<<`, `>>`)

Bit shifting is a hardware-level shortcut for multiplying or dividing by powers of 2.

# Multiply by 2^3 (8)
x = 5
print(x << 3) # 40

# Divide by 2^1 (2)
y = 10
print(y >> 1) # 5

Common Pitfalls

Operator Precedence: Bitwise operators have lower precedence than arithmetic operators, but higher precedence than comparison operators. This leads to extremely common bugs.

x = 5
# BAD: Evaluates to x & (1 == 1) -> x & True -> x & 1 -> 1
if x & 1 == 1: 
    pass

# GOOD: Always use parentheses around bitwise operations!
if (x & 1) == 1:
    pass

Key Takeaways

Use & 1 to check if a number is odd/even.
Use << to quickly multiply by powers of 2.
Use >> to quickly divide by powers of 2.
Always use parentheses when combining bitwise operations with ==, !=, <, or >.