Multi-channel ADC scanning in Embedded C - Time & Space Complexity

Time Complexity: Multi-channel ADC scanning

O(n)

Understanding Time Complexity

When reading multiple sensors using an ADC, the time it takes depends on how many channels we scan.

We want to know how the scanning time grows as we add more channels.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void scanADC(int *channels, int numChannels, int *results) {
    for (int i = 0; i < numChannels; i++) {
        results[i] = readADC(channels[i]);
    }
}

int readADC(int channel) {
    // Simulate ADC read delay
    // Returns analog value for the channel
    return channel * 10; // placeholder
}
    

This code reads analog values from multiple ADC channels one by one and stores the results.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that calls readADC for each channel.
• How many times: Exactly once per channel, so numChannels times.

How Execution Grows With Input

Each additional channel adds one more ADC read operation, so the total work grows steadily.

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

Pattern observation: The time grows directly in proportion to the number of channels scanned.

Final Time Complexity

Time Complexity: O(n)

This means the scanning time increases linearly as you add more ADC channels.

Common Mistake

[X] Wrong: "Reading multiple ADC channels happens all at once, so time stays the same no matter how many channels."

[OK] Correct: Each channel requires a separate read operation, so time adds up with each channel scanned.

Interview Connect

Understanding how scanning multiple sensors affects time helps you design efficient embedded systems and shows you can think about performance in real hardware tasks.

Self-Check

"What if we used DMA to read all ADC channels in parallel? How would the time complexity change?"

Practice

1.

What is the main purpose of multi-channel ADC scanning in embedded C?

easy

A. To read multiple analog inputs one after another automatically

B. To write digital output signals to multiple pins

C. To increase the clock speed of the microcontroller

D. To store data in external memory

Solution

1. Step 1: Understand ADC scanning concept

   Multi-channel ADC scanning reads several analog inputs sequentially without manual switching.

2. Step 2: Identify the purpose

   This allows efficient sensor data collection from multiple sources automatically.

3. Final Answer:

   To read multiple analog inputs one after another automatically -> Option A

4. Quick Check:

   Multi-channel ADC scanning = reading multiple analog inputs [OK]

Hint: Remember ADC scanning reads many inputs in sequence [OK]

Common Mistakes:

• Confusing ADC scanning with digital output control
• Thinking it speeds up the microcontroller clock
• Assuming it stores data externally

2.

Which of the following code snippets correctly initializes a multi-channel ADC scan for 3 channels in embedded C?

void ADC_Init() {
    ADCON0 = 0x01; // Enable ADC
    ADCON1 = 0x00; // Configure ports as analog
    ADCON2 = 0xA9; // Right justify, 12 TAD, Fosc/8
    // Missing code here
}

easy

A. ADCHS = 0x00; // Select channel 0 only

B. ADCHS = 0x03; // Select channels 0 and 1 only

C. ADCHS = 0xFF; // Select all channels

D. ADCHS = 0x07; // Select channels 0 to 2 for scanning

Solution

1. Step 1: Understand ADCHS register role

   ADCHS selects which ADC channels to scan; bits 0-2 correspond to channels 0-2.

2. Step 2: Choose correct bitmask for 3 channels

   0x07 in binary is 00000111, enabling channels 0,1,2 for scanning.

3. Final Answer:

   ADCHS = 0x07; // Select channels 0 to 2 for scanning -> Option D

4. Quick Check:

   0x07 = channels 0,1,2 selected [OK]

Hint: Use bitmask 0x07 to select first 3 ADC channels [OK]

Common Mistakes:

• Selecting only one channel instead of multiple
• Using 0xFF which may select invalid channels
• Confusing ADCHS with ADCON registers

3.

Consider the following embedded C code snippet for multi-channel ADC scanning:

int adc_values[3];
for(int ch = 0; ch < 3; ch++) {
    ADCON0 = (ch << 2) | 0x01; // Select channel and turn on ADC
    __delay_ms(2); // Acquisition time
    ADCON0 |= 0x02; // Start conversion
    while(ADCON0 & 0x02); // Wait for conversion
    adc_values[ch] = (ADRESH << 8) | ADRESL;
}

What will be the content of adc_values after this loop?

medium

A. Array with zeros because ADC is not started

B. Array with ADC readings from channels 0, 1, and 2

C. Array with same value repeated 3 times

D. Compilation error due to wrong bit operations

Solution

1. Step 1: Analyze loop operation

   The loop runs for ch = 0 to 2, selecting each ADC channel and starting conversion.

2. Step 2: Understand ADC reading storage

   After conversion, the 10-bit ADC result is stored in adc_values[ch] for each channel.

3. Final Answer:

   Array with ADC readings from channels 0, 1, and 2 -> Option B

4. Quick Check:

   Loop reads channels 0-2 storing results in array [OK]

Hint: Loop reads and stores ADC values channel-wise [OK]

Common Mistakes:

• Assuming ADC conversion never starts
• Thinking all values are identical
• Misreading bitwise operations as errors

4.

Identify the error in this multi-channel ADC scanning code snippet:

for(int i = 0; i < 3; i++) {
    ADCON0 = (i << 2); // Select channel
    ADCON0 |= 0x01; // Turn on ADC
    ADCON0 |= 0x02; // Start conversion
    while(ADCON0 & 0x02);
    adc_results[i] = (ADRESH << 8) | ADRESL;
}

medium

A. The ADC result is stored incorrectly

B. The conversion start bit is never set

C. ADCON0 is overwritten before turning on ADC, losing previous bits

D. The loop runs one time too many

Solution

1. Step 1: Check ADCON0 assignment

   ADCON0 is assigned with (i << 2), which clears other bits including ADC enable.

2. Step 2: Understand bitwise OR usage

   Turning on ADC with |= 0x01 works, but previous bits are lost due to overwrite.

3. Final Answer:

   ADCON0 is overwritten before turning on ADC, losing previous bits -> Option C

4. Quick Check:

   Overwriting ADCON0 clears important bits [OK]

Hint: Use |= to set bits, not = to overwrite [OK]

Common Mistakes:

• Ignoring that ADCON0 bits get reset
• Thinking start bit is not set
• Miscounting loop iterations
• Misunderstanding ADC result storage

5.

You want to scan 4 analog sensors using a microcontroller ADC that supports hardware scanning. Which approach best improves efficiency?

// Option 1: Manually switch channels in software loop
// Option 2: Enable hardware scan mode and read results from buffer
// Option 3: Use single channel repeatedly
// Option 4: Use digital inputs instead

hard

A. Use hardware scan mode and read results from buffer

B. Manually switch channels in software loop

C. Use single channel repeatedly with delays

D. Use digital inputs instead of ADC

Solution

1. Step 1: Compare manual vs hardware scanning

   Manual switching requires CPU cycles and delays; hardware scan automates channel switching.

2. Step 2: Identify efficiency gain

   Hardware scan mode reads multiple channels automatically, storing results in buffer for quick access.

3. Step 3: Evaluate other options

   Using single channel repeatedly or digital inputs does not meet multi-channel analog reading needs efficiently.

4. Final Answer:

   Use hardware scan mode and read results from buffer -> Option A

5. Quick Check:

   Hardware scan mode = efficient multi-channel ADC reading [OK]

Hint: Hardware scan automates multi-channel ADC reading [OK]

Common Mistakes:

• Choosing manual switching which wastes CPU time
• Using single channel repeatedly causing delays
• Confusing digital inputs with analog ADC inputs