Single channel ADC reading in Embedded C - Time & Space Complexity

Time Complexity: Single channel ADC reading

O(n)

Understanding Time Complexity

We want to understand how the time to read from an ADC changes as we take more readings.

How does the number of readings affect the total time spent?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int readADC(int channel) {
    // Start ADC conversion
    ADC_START_CONVERSION(channel);
    
    // Wait until conversion is done
    while(!ADC_CONVERSION_COMPLETE());
    
    // Return the ADC value
    return ADC_GET_VALUE();
}

int readMultiple(int channel, int times) {
    int sum = 0;
    for(int i = 0; i < times; i++) {
        sum += readADC(channel);
    }
    return sum / times;
}
    

This code reads an analog value from one ADC channel multiple times and averages the results.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop in readMultiple calls readADC repeatedly.
• How many times: Exactly times times, which is the input size.

How Execution Grows With Input

Each additional reading adds one full ADC read cycle, so time grows directly with the number of readings.

Input Size (times)	Approx. Operations
10	10 ADC reads
100	100 ADC reads
1000	1000 ADC reads

Pattern observation: Doubling the number of readings doubles the total time.

Final Time Complexity

Time Complexity: O(n)

This means the total time grows linearly with the number of ADC readings requested.

Common Mistake

[X] Wrong: "Reading multiple times is just as fast as reading once because the ADC is fast."

[OK] Correct: Each ADC read takes time to start, convert, and finish, so multiple reads add up in time.

Interview Connect

Understanding how repeated hardware reads affect time helps you write efficient embedded code and explain your reasoning clearly.

Self-Check

"What if we read from multiple ADC channels instead of one? How would the time complexity change?"