Generating precise delays with timers in Embedded C - Time & Space Complexity

Time Complexity: Generating precise delays with timers

O(n)

Understanding Time Complexity

When using timers to create delays in embedded C, it's important to understand how the time the program takes grows as the delay length changes.

We want to know how the program's running time changes when we ask for longer or shorter delays.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void delay_ms(int ms) {
    for (int i = 0; i < ms; i++) {
        for (int j = 0; j < 1000; j++) {
            // empty loop to waste time
        }
    }
}
    

This code creates a delay by running two nested loops: the outer loop runs once per millisecond, and the inner loop runs 1000 times to waste time.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The inner empty loop that runs 1000 times.
• How many times: The inner loop runs 1000 times for each iteration of the outer loop, which runs ms times.

How Execution Grows With Input

As the delay time ms increases, the total number of loop operations grows proportionally.

Input Size (ms)	Approx. Operations
10	10 x 1000 = 10,000
100	100 x 1000 = 100,000
1000	1000 x 1000 = 1,000,000

Pattern observation: The total operations increase directly with the delay time requested.

Final Time Complexity

Time Complexity: O(n)

This means the time the program takes grows in a straight line with the delay length you ask for.

Common Mistake

[X] Wrong: "The delay time does not affect how long the program runs because the loops are fixed."

[OK] Correct: The outer loop runs once per millisecond, so increasing the delay increases the total loops and time proportionally.

Interview Connect

Understanding how delay loops scale helps you reason about timing and efficiency in embedded systems, a key skill for writing reliable code.

Self-Check

"What if we replaced the inner loop with a hardware timer interrupt instead? How would the time complexity change?"

Practice

1. What is the main purpose of using timers in embedded C programming for delays?

easy

A. To create precise and accurate wait times without blocking the CPU

B. To increase the CPU clock speed automatically

C. To store large amounts of data temporarily

D. To handle user input events directly

Solution

1. Step 1: Understand timer functionality

   Timers count clock pulses to measure time intervals precisely without busy-waiting.

2. Step 2: Identify timer use for delays

   Using timers allows the program to wait exact times while freeing CPU for other tasks.

3. Final Answer:

   To create precise and accurate wait times without blocking the CPU -> Option A

4. Quick Check:

   Timers = precise delays [OK]

Hint: Timers count clock pulses for exact delays [OK]

Common Mistakes:

• Thinking timers speed up the CPU
• Confusing timers with memory storage
• Assuming timers handle user input

2. Which of the following is the correct way to start a hardware timer in embedded C?

easy

A. beginTimer();

B. start_timer();

C. timer_start();

D. initTimer();

Solution

1. Step 1: Recognize common timer function names

   Standard embedded C libraries often use timer_start() to begin timers.

2. Step 2: Check syntax correctness

   timer_start(); is a valid function call matching typical timer APIs.

3. Final Answer:

   timer_start(); -> Option C

4. Quick Check:

   Correct timer start syntax = timer_start() [OK]

Hint: Look for standard function names like timer_start() [OK]

Common Mistakes:

• Using incorrect function names like start_timer()
• Confusing initialization with starting
• Missing parentheses in function calls

3. Given the code snippet:

timer_set(1000); // Set timer for 1000 ms
timer_start();
while(!timer_expired()) {
  // wait
}
LED_toggle();

What happens after this code runs?

medium

A. LED toggles immediately without delay

B. LED toggles after approximately 1 second delay

C. LED never toggles because timer_expired() is always false

D. LED toggles after 1000 CPU cycles, not milliseconds

Solution

1. Step 1: Understand timer_set and timer_start

   The timer is set for 1000 milliseconds and then started to count down.

2. Step 2: Analyze the while loop waiting for timer expiration

   The loop waits until timer_expired() returns true, which happens after ~1 second.

3. Final Answer:

   LED toggles after approximately 1 second delay -> Option B

4. Quick Check:

   timer_set(1000) = 1 second delay [OK]

Hint: timer_set(ms) delays for ms milliseconds [OK]

Common Mistakes:

• Assuming timer_expired() never becomes true
• Confusing CPU cycles with milliseconds
• Thinking LED toggles immediately

4. Identify the error in this delay code:

timer_set(500);
while(timer_expired()) {
  // wait
}
LED_on();

medium

A. timer_expired() function does not exist

B. timer_set() should be called after the while loop

C. LED_on() should be called before timer_set()

D. The while condition should be !timer_expired() to wait correctly

Solution

1. Step 1: Analyze the while loop condition

   The loop waits while timer_expired() is true, but timer just set, so expired is false initially.

2. Step 2: Correct the condition to wait until timer expires

   It should wait while timer is NOT expired, so condition must be negated: !timer_expired().

3. Final Answer:

   The while condition should be !timer_expired() to wait correctly -> Option D

4. Quick Check:

   Wait while not expired = !timer_expired() [OK]

Hint: Wait while timer not expired: use !timer_expired() [OK]

Common Mistakes:

• Using timer_expired() without negation in wait loop
• Calling timer_set() after waiting
• Assuming LED_on() order affects delay

5. You want to toggle an LED every 250 ms precisely using a timer interrupt. Which approach is best?

hard

A. Use a timer interrupt set for 250 ms to toggle LED inside ISR

B. Use a busy-wait loop with delay function for 250 ms repeatedly

C. Toggle LED once and never use timer

D. Use a timer interrupt but toggle LED outside ISR only

Solution

1. Step 1: Understand precise timing with interrupts

   Using timer interrupts allows exact timing without blocking CPU.

2. Step 2: Identify best place to toggle LED

   Toggling LED inside the timer ISR ensures it happens exactly every 250 ms.

3. Final Answer:

   Use a timer interrupt set for 250 ms to toggle LED inside ISR -> Option A

4. Quick Check:

   Timer ISR toggles LED precisely every 250 ms [OK]

Hint: Toggle LED inside timer ISR for precise periodic delay [OK]

Common Mistakes:

• Using busy-wait loops causing CPU blocking
• Toggling LED outside ISR losing timing precision
• Not using timer interrupts for periodic tasks