I2C acknowledge and NACK behavior in Embedded C - Time & Space Complexity

Time Complexity: I2C acknowledge and NACK behavior

O(n)

Understanding Time Complexity

When working with I2C communication, it is important to understand how acknowledge (ACK) and not-acknowledge (NACK) signals affect the flow of data.

We want to see how the time taken changes as the number of bytes sent or received grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Send bytes over I2C and check ACK/NACK
for (int i = 0; i < length; i++) {
    I2C_SendByte(data[i]);
    if (!I2C_WaitAck()) {
        // NACK received, stop sending
        break;
    }
}

This code sends bytes one by one over I2C and stops if a NACK is received.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Sending each byte and waiting for ACK/NACK.
• How many times: Up to length times, but may stop early if NACK occurs.

How Execution Grows With Input

As the number of bytes to send increases, the number of send-and-wait steps grows roughly the same.

Input Size (length)	Approx. Operations
10	Up to 10 send-and-wait steps
100	Up to 100 send-and-wait steps
1000	Up to 1000 send-and-wait steps

Pattern observation: The time grows linearly with the number of bytes sent, unless a NACK stops the process early.

Final Time Complexity

Time Complexity: O(n)

This means the time taken grows in direct proportion to the number of bytes sent over I2C.

Common Mistake

[X] Wrong: "The time to send data over I2C is always constant regardless of data size."

[OK] Correct: Each byte requires sending and waiting for an ACK or NACK, so more bytes mean more time.

Interview Connect

Understanding how communication protocols like I2C handle acknowledgments helps you reason about timing and reliability in embedded systems.

Self-Check

"What if the code always waits for an ACK but never stops on NACK? How would the time complexity change?"

Practice

1. What does an ACK (Acknowledge) signal mean in I2C communication?

easy

A. The sender is requesting to resend the data

B. The receiver wants to stop communication immediately

C. The communication line is idle

D. The receiver successfully received data and is ready for more

Solution

1. Step 1: Understand ACK meaning in I2C

   ACK means the receiver signals it has received the data correctly and is ready to continue.

2. Step 2: Compare options with ACK meaning

   Only The receiver successfully received data and is ready for more matches this meaning; others describe stop or errors.

3. Final Answer:

   The receiver successfully received data and is ready for more -> Option D

4. Quick Check:

   ACK = Ready for more data [OK]

Hint: ACK means receiver says 'send more' [OK]

Common Mistakes:

• Confusing ACK with NACK meaning
• Thinking ACK means stop communication
• Assuming ACK means error occurred

2. Which of the following code snippets correctly sends a NACK after reading the last byte in I2C using embedded C?

easy

A. i2c_read_byte(I2C1, ACK);

B. i2c_read_byte(I2C1, NACK);

C. i2c_write_byte(I2C1, NACK);

D. i2c_send_ack(I2C1);

Solution

1. Step 1: Identify correct function to read with NACK

   To signal no more data is needed, the read function must be called with NACK.

2. Step 2: Check options for correct usage

   i2c_read_byte(I2C1, NACK); uses i2c_read_byte with NACK, which is correct. Others either send ACK or write instead of read.

3. Final Answer:

   i2c_read_byte(I2C1, NACK); -> Option B

4. Quick Check:

   Read last byte with NACK to stop [OK]

Hint: Use read with NACK to stop reading last byte [OK]

Common Mistakes:

• Using ACK instead of NACK after last byte
• Calling write instead of read for NACK
• Confusing function names for ACK/NACK

3. Consider this code snippet reading 3 bytes from an I2C device:

for (int i = 0; i < 3; i++) {
  data[i] = (i < 2) ? i2c_read_byte(I2C1, ACK) : i2c_read_byte(I2C1, NACK);
}

What is the purpose of sending NACK on the last byte?

medium

A. To request the device to resend the last byte

B. To acknowledge the last byte and continue reading

C. To indicate the master will stop reading after this byte

D. To reset the I2C bus immediately

Solution

1. Step 1: Analyze the loop and ACK/NACK usage

   The loop reads 3 bytes; for first two bytes it sends ACK, for last byte it sends NACK.

2. Step 2: Understand NACK meaning on last byte

   NACK signals the master will stop reading after this byte, telling the slave no more data is needed.

3. Final Answer:

   To indicate the master will stop reading after this byte -> Option C

4. Quick Check:

   NACK on last byte = stop reading [OK]

Hint: NACK on last byte means stop reading [OK]

Common Mistakes:

• Thinking NACK requests resend
• Assuming NACK resets bus
• Confusing ACK and NACK roles

4. You wrote this code to read bytes from I2C but the slave device never stops sending data:

for (int i = 0; i < 4; i++) {
  data[i] = i2c_read_byte(I2C1, ACK);
}

What is the likely problem?

medium

A. You never sent NACK after the last byte to stop reading

B. You should use i2c_write_byte instead of i2c_read_byte

C. The loop should run 5 times instead of 4

D. You need to send a STOP condition before reading

Solution

1. Step 1: Check ACK/NACK usage in the loop

   The code sends ACK for every byte read, never sending NACK to signal stop.

2. Step 2: Understand effect of missing NACK

   Without NACK after last byte, slave keeps sending data, causing endless transmission.

3. Final Answer:

   You never sent NACK after the last byte to stop reading -> Option A

4. Quick Check:

   Missing NACK means no stop signal [OK]

Hint: Send NACK after last byte to stop slave [OK]

Common Mistakes:

• Using ACK for all bytes including last
• Confusing read and write functions
• Ignoring need for STOP condition after read

5. You want to write a function that reads a variable number of bytes from an I2C device and properly sends ACK for all bytes except the last one, which should send NACK. Which code snippet correctly implements this behavior?

hard

A. for (int i = 0; i < length - 1; i++) {
data[i] = i2c_read_byte(I2C1, ACK);
}
data[length - 1] = i2c_read_byte(I2C1, NACK);

B. for (int i = 0; i < length; i++) {
data[i] = i2c_read_byte(I2C1, ACK);
}

C. for (int i = 0; i < length; i++) {
data[i] = i2c_read_byte(I2C1, NACK);
}

D. data[0] = i2c_read_byte(I2C1, NACK);
for (int i = 1; i < length; i++) {
data[i] = i2c_read_byte(I2C1, ACK);
}

Solution

1. Step 1: Understand ACK/NACK pattern for multiple bytes

   All bytes except last must be read with ACK; last byte with NACK to stop.

2. Step 2: Analyze each option

   for (int i = 0; i < length - 1; i++) { data[i] = i2c_read_byte(I2C1, ACK); } data[length - 1] = i2c_read_byte(I2C1, NACK); reads all but last byte with ACK, then last byte with NACK, correctly signaling stop. Others send wrong signals or in wrong order.

3. Final Answer:

   for (int i = 0; i < length - 1; i++) { data[i] = i2c_read_byte(I2C1, ACK); } data[length - 1] = i2c_read_byte(I2C1, NACK); -> Option A

4. Quick Check:

   ACK all but last, NACK last byte [OK]

Hint: Send NACK only on last byte read [OK]

Common Mistakes:

• Sending NACK on all bytes
• Sending ACK on last byte
• Reading last byte first with NACK