Bitwise Operators

Bitwise operators work on integers bit by bit. Python converts each integer to binary, performs the operation, and returns the result as a decimal integer.

Important: Bitwise operators do not work on floats.

What you'll learn

• The six bitwise operators
• Why floats raise TypeError
• Difference between & and and
• Bitwise operations on sets
• Why ~n = -(n + 1)

How bitwise operators work

Python follows three steps:

1. Convert the integer to binary
2. Apply the bitwise operation
3. Convert the result back to decimal

Example:

10  →  1010₂
4   →  0100₂
----------------
AND →  0000₂
Result = 0

The six bitwise operators

Symbol	Name	Purpose
<<	Left shift	Move bits left
>>	Right shift	Move bits right
&	AND	Both bits must be 1
|	OR	Either bit is 1
^	XOR	Bits are different
~	Complement	Invert every bit

Left shift (<<)

Left shift moves bits left and fills zeros on the right.

Each left shift by 1 multiplies by 2. Example: 10 << 3 = 80.

print(10 << 3)   # 80
print(4 << 3)    # 32
print(9 << 2)    # 36
print(10 << 0)   # 10

Invalid:

# 10.3 << 2   → TypeError
# 4 << -1     → ValueError

Right shift (>>)

Right shift removes bits from the right.

print(10 >> 3)   # 1
print(16 >> 2)   # 4
print(32 >> 3)   # 4
print(32 >> 0)   # 32

For positive integers, >> 3 is like dividing by 8 (when bits do not get lost).

AND (&)

AND returns 1 only when both bits are 1.

A	B	A & B
0	0	0
0	1	0
1	0	0
1	1	1

print(10 & 4)      # 0
print(5 & 4)       # 4

print(10 and 4)    # 4  — logical and, not bitwise

# 10.2 & 2   → TypeError

& is bitwise. and is logical — they solve different problems.

OR (|)

OR returns 1 if either bit is 1.

print(10 | 4)    # 14

Binary: 00001010 | 00000100 = 00001110

XOR (^)

XOR returns 1 when bits are different.

A	B	A ^ B
0	0	0
0	1	1
1	0	1
1	1	0

print(2 ^ 3)      # 1
print(10 ^ 15)    # 5

Complement (~)

Complement flips every bit. The formula to memorize:

~n = -(n + 1)

print(~10)       # -11
print(~100)      # -101
print(~(-123))   # 122

Bitwise operators on sets

The same symbols have a different meaning for sets:

s1 = {10, 20, 30}
s2 = {15, 20, 35}

print(s1 & s2)   # {20}           intersection
print(s1 | s2)   # {10, 15, 20, 30, 35}   union
print(s1 ^ s2)   # {10, 15, 30, 35}       symmetric difference

& vs and

Operator	Purpose	Example
&	Bitwise / set intersection	10 & 4 → 0
and	Logical operator	10 and 4 → 4

print(10 & 4)      # 0
print(10 and 4)    # 4

The results differ because the operators answer different questions.

Practice exercises

Exercise 1 — Predict before running:

10 << 3
10 >> 3

Which multiplies by 8? Which divides by 8 (for this value)?

Exercise 2 — Compare:

10 & 4
10 and 4

Explain why the outputs differ.

Exercise 3 — Use the formula:

~25

Calculate manually with -(n + 1) before checking in Python.

Quick knowledge check

1. Can you use bitwise shift on a float?
   No. It raises TypeError.

2. What is the complement formula?
   ~n = -(n + 1)

3. Is & the same as and?
   No. & is bitwise (or set intersection); and is logical.

Summary

• Bitwise operators work on integers (not floats).
• Python provides six operators: <<, >>, &, |, ^, and ~.
• Shifts reject floats and negative shift counts.
• &, |, and ^ also work with sets as intersection, union, and symmetric difference.
• Memorize ~n = -(n + 1).

Next lesson: Membership Operators (in / not in) — check whether values exist inside strings, lists, dictionaries, and sets.