Time Complexity: XOR for toggling bits
O(1)
0
0
XOR for toggling bits in Embedded C - Time & Space Complexity
Understanding Time Complexity
We want to see how the time to toggle bits changes as the number of bits grows.
How does the work needed grow when we toggle more bits?
Scenario Under Consideration
Analyze the time complexity of the following code snippet.
void toggle_bits(unsigned int *num, unsigned int mask) {
*num = *num ^ mask;
}
This code toggles bits in a number using XOR with a mask.
Identify Repeating Operations
Identify the loops, recursion, array traversals that repeat.
- Primary operation: One XOR operation on the whole number.
- How many times: Exactly once per call, no loops or recursion.
How Execution Grows With Input
The time to toggle bits stays the same no matter how many bits we have.
| Input Size (bits) | Approx. Operations |
|---|---|
| 8 | 1 XOR operation |
| 32 | 1 XOR operation |
| 64 | 1 XOR operation |
Pattern observation: The operation count does not increase with input size.
Final Time Complexity
Time Complexity: O(1)
This means toggling bits takes the same amount of time no matter how many bits are involved.
Common Mistake
[X] Wrong: "Toggling more bits means more time because each bit changes separately."
[OK] Correct: XOR toggles all bits in one step using a single operation, so time does not grow with bit count.
Interview Connect
Understanding how bitwise operations work efficiently shows you know how low-level code runs fast, a useful skill in many embedded and systems tasks.
Self-Check
"What if we toggled bits one by one in a loop instead of using XOR? How would the time complexity change?"