Why ADC is needed in Embedded C - Performance Analysis

Time Complexity: Why ADC is needed

O(1)

Understanding Time Complexity

We want to understand how the time to convert analog signals to digital changes as input size or precision changes.

How does the ADC process time grow when we change its settings or input?

Scenario Under Consideration

Analyze the time complexity of the following ADC conversion code snippet.

// Start ADC conversion
ADC_StartConversion();

// Wait until conversion is complete
while(!ADC_ConversionComplete()) {
  ; // busy wait
}

// Read ADC result
int result = ADC_ReadResult();

This code starts an ADC conversion, waits for it to finish, then reads the digital value.

Identify Repeating Operations

Look for loops or repeated checks in the code.

• Primary operation: The while loop that waits for conversion to complete.
• How many times: It runs until the ADC finishes converting one analog value.

How Execution Grows With Input

The waiting time depends on the ADC resolution and clock speed, not on input size like arrays.

Input Size (n)	Approx. Operations
10 (low resolution)	Short wait, few loop checks
100 (medium resolution)	Longer wait, more loop checks
1000 (high resolution)	Even longer wait, many loop checks

Pattern observation: The time grows roughly with the ADC resolution setting, not with data size.

Final Time Complexity

Time Complexity: O(1)

This means the conversion time is constant for each reading, independent of data size.

Common Mistake

[X] Wrong: "ADC conversion time grows with the amount of data to convert."

[OK] Correct: ADC converts one analog value at a time, so each conversion takes a fixed time regardless of data size.

Interview Connect

Understanding ADC timing helps you explain how embedded systems handle real-world signals efficiently and predictably.

Self-Check

"What if we changed the ADC resolution to a higher bit count? How would the conversion time change?"