Writing to a hardware register in Embedded C - Time & Space Complexity

Time Complexity: Writing to a hardware register

O(n)

Understanding Time Complexity

When writing to a hardware register, it's important to know how the time needed changes as the program runs.

We want to see how the number of write operations grows with the input size.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

volatile uint32_t *REG = (volatile uint32_t *)0x40021000;

void write_values(uint32_t *values, int n) {
    for (int i = 0; i < n; i++) {
        *REG = values[i];
    }
}
    

This code writes each value from an array to a hardware register one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Writing a value to the hardware register inside the loop.
• How many times: Exactly once for each element in the input array, so n times.

How Execution Grows With Input

Each new value in the input array causes one write operation to the register.

Input Size (n)	Approx. Operations
10	10 writes
100	100 writes
1000	1000 writes

Pattern observation: The number of writes grows directly with the number of input values.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete writing grows in direct proportion to the number of values.

Common Mistake

[X] Wrong: "Writing to a hardware register is always constant time no matter how many values."

[OK] Correct: Each write operation takes time, so writing multiple values adds up linearly.

Interview Connect

Understanding how loops affect time helps you explain how embedded code interacts with hardware efficiently.

Self-Check

"What if we added a nested loop writing the same values multiple times? How would the time complexity change?"