Sensor reading through ADC (temperature, light) in Embedded C - Time & Space Complexity

Time Complexity: Sensor reading through ADC (temperature, light)

O(n)

Understanding Time Complexity

When reading sensors using ADC, it is important to know how the time to get data changes as we read more samples.

We want to see how the program's work grows when reading multiple sensor values.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Read multiple sensor values using ADC
void readSensors(int *buffer, int count) {
    for (int i = 0; i < count; i++) {
        buffer[i] = readADC(); // Read one sensor value
    }
}

int readADC() {
    // Simulate ADC reading delay
    return 42; // Dummy sensor value
}
    

This code reads sensor values one by one and stores them in a buffer.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that calls readADC() repeatedly.
• How many times: Exactly count times, once per sensor reading.

How Execution Grows With Input

Each additional sensor reading adds one more call to readADC(), so work grows steadily.

Input Size (count)	Approx. Operations
10	10 calls to readADC()
100	100 calls to readADC()
1000	1000 calls to readADC()

Pattern observation: The total work grows directly with the number of readings.

Final Time Complexity

Time Complexity: O(n)

This means if you double the number of sensor readings, the time to complete also roughly doubles.

Common Mistake

[X] Wrong: "Reading multiple sensors happens instantly and does not add time."

[OK] Correct: Each sensor reading takes time, so more readings mean more total time.

Interview Connect

Understanding how sensor reading time grows helps you design efficient embedded programs and explain your code clearly in interviews.

Self-Check

"What if we read sensors in parallel instead of one by one? How would the time complexity change?"

Practice

1. What is the main purpose of using an ADC (Analog-to-Digital Converter) in embedded systems when reading sensors like temperature or light?
ADC converts:

easy

A. Analog sensor signals into digital values the microcontroller can process

B. Digital signals into analog voltages for sensors

C. Temperature readings directly into Celsius values

D. Light intensity into sound signals

Solution

1. Step 1: Understand ADC function

   ADC changes continuous analog signals from sensors into digital numbers.

2. Step 2: Match function to options

   Only Analog sensor signals into digital values the microcontroller can process correctly describes converting analog sensor signals to digital values.

3. Final Answer:

   Analog sensor signals into digital values the microcontroller can process -> Option A

4. Quick Check:

   ADC converts analog to digital [OK]

Hint: Remember: ADC means Analog to Digital Converter [OK]

Common Mistakes:

• Confusing ADC with DAC (Digital-to-Analog Converter)
• Thinking ADC outputs temperature directly
• Assuming ADC converts digital to analog

2. Which of the following is the correct way to start an ADC conversion on channel 3 in embedded C?

ADC_StartConversion(____);

easy

A. 3

B. "3"

C. channel3

D. ADC_Channel_3

Solution

1. Step 1: Identify correct channel constant

   Embedded C ADC functions usually use predefined constants like ADC_Channel_3 for clarity.

2. Step 2: Check options for proper syntax

   ADC_Channel_3 uses the correct constant; others are either raw numbers or strings, which are incorrect.

3. Final Answer:

   ADC_Channel_3 -> Option D

4. Quick Check:

   Use predefined channel constants [OK]

Hint: Use ADC_Channel_x constants, not raw numbers or strings [OK]

Common Mistakes:

• Passing channel number as string
• Using raw integers without constants
• Using undefined variable names

3. Given this code snippet reading ADC value from a temperature sensor:

int adc_value = ADC_Read(ADC_Channel_1);
float voltage = (adc_value / 1023.0) * 5.0;
float temperature = (voltage - 0.5) * 100;
printf("Temp: %.1f C\n", temperature);

What will be the output if adc_value is 216?

medium

A. Temp: 60.0 C

B. Temp: 55.0 C

C. Temp: 55.5 C

D. Temp: 50.0 C

Solution

1. Step 1: Compute voltage from adc_value

   voltage = (216 / 1023.0) * 5.0 ≈ 1.055 V

2. Step 2: Compute temperature from voltage

   temperature = (1.055 - 0.5) * 100 = 55.5 °C

3. Step 3: Format output with printf

   %.1f formats 55.5 as "55.5", so output is "Temp: 55.5 C"

4. Final Answer:

   Temp: 55.5 C -> Option C

5. Quick Check:

   (adc / 1023.0 * 5.0 - 0.5) * 100 ≈ 55.5 [OK]

Hint: Calculate voltage first, then apply temperature formula [OK]

Common Mistakes:

• Using integer division instead of float
• Forgetting to subtract 0.5V before multiplying
• Mixing up ADC max value (1023) and voltage reference

4. Identify the error in this code snippet intended to read light sensor value and print voltage:

int adc_val = ADC_Read(ADC_Channel_2);
float voltage = adc_val / 1023 * 3.3;
printf("Voltage: %.2f V\n", voltage);

medium

A. Integer division causes voltage to be zero

B. printf format specifier should be %d instead of %f

C. Incorrect ADC channel used for light sensor

D. Missing semicolon after ADC_Read call

Solution

1. Step 1: Analyze division operation

   adc_val and 1023 are integers, so adc_val / 1023 does integer division, which truncates to 0 if adc_val < 1023.

2. Step 2: Effect on voltage calculation

   Integer division results in 0 or 1, so voltage becomes 0 or 3.3 incorrectly.

3. Final Answer:

   Integer division causes voltage to be zero -> Option A

4. Quick Check:

   Use float division to avoid zero voltage [OK]

Hint: Cast numerator or denominator to float before division [OK]

Common Mistakes:

• Forgetting to cast to float
• Assuming integer division works for floats
• Using wrong printf format specifier

5. You want to read both temperature and light sensors using ADC channels 1 and 2 respectively. Which code snippet correctly reads both sensors and converts their ADC values to voltages assuming 10-bit ADC and 3.3V reference?

int temp_adc = ADC_Read(ADC_Channel_1);
int light_adc = ADC_Read(ADC_Channel_2);
float temp_voltage = (float)temp_adc / 1023 * 3.3;
float light_voltage = (float)light_adc / 1023 * 3.3;

hard

A. Should divide by 1024 instead of 1023 for voltage calculation

B. Correct as is, both readings converted properly

C. Missing ADC initialization before reading sensors

D. ADC_Read should be called only once for both sensors

Solution

1. Step 1: Check ADC reading and conversion

   ADC_Read called separately for each channel, storing in int variables.

2. Step 2: Voltage conversion uses float cast and divides by 1023 (max ADC value for 10-bit), multiplied by 3.3V reference.

   This is correct for 10-bit ADC.

3. Final Answer:

   Correct as is, both readings converted properly -> Option B

4. Quick Check:

   Separate reads and float division with 1023 max value [OK]

Hint: Cast ADC value to float before division for accurate voltage [OK]

Common Mistakes:

• Dividing by 1024 instead of 1023
• Not initializing ADC before reading
• Trying to read both sensors with one ADC_Read call