Scaling analog values in PLC Programming - Time & Space Complexity

Time Complexity: Scaling analog values

O(n)

Understanding Time Complexity

When scaling analog values in PLC programming, it is important to know how the time to process changes as the number of values grows.

We want to see how the work done grows when more values need scaling.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

FOR i := 0 TO n-1 DO
  scaledValue[i] := (rawValue[i] - inputMin) * (outputMax - outputMin) / (inputMax - inputMin) + outputMin;
END_FOR

This code scales each raw analog input value to a new range, processing all values one by one.

Identify Repeating Operations

• Primary operation: The FOR loop that scales each value.
• How many times: Exactly n times, once for each input value.

How Execution Grows With Input

Each new input value adds one more scaling operation, so the total work grows directly with n.

Input Size (n)	Approx. Operations
10	10 scaling calculations
100	100 scaling calculations
1000	1000 scaling calculations

Pattern observation: The work increases evenly as the number of values increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to scale values grows in direct proportion to how many values there are.

Common Mistake

[X] Wrong: "Scaling multiple values takes the same time no matter how many values there are."

[OK] Correct: Each value needs its own calculation, so more values mean more work and more time.

Interview Connect

Understanding how loops affect time helps you explain how your code handles larger data sets efficiently and clearly.

Self-Check

What if we added a nested loop inside the FOR loop to process each value multiple times? How would the time complexity change?

Practice

1. What is the main purpose of scaling analog values in PLC programming?

easy

A. To reduce the size of the PLC program

B. To increase the speed of the PLC processor

C. To convert raw sensor signals into meaningful engineering units

D. To change digital signals into analog signals

Solution

1. Step 1: Understand analog input signals

   Raw sensor signals are usually voltage or current values that need interpretation.

2. Step 2: Purpose of scaling

   Scaling converts these raw signals into meaningful units like temperature or pressure.

3. Final Answer:

   To convert raw sensor signals into meaningful engineering units -> Option C

4. Quick Check:

   Scaling = Convert raw to useful units [OK]

Hint: Scaling means converting raw sensor data to real-world units [OK]

Common Mistakes:

• Confusing scaling with speeding up the PLC
• Thinking scaling reduces program size
• Mixing analog and digital signal conversion

2. Which of the following is the correct formula to scale a raw analog input raw from range raw_min to raw_max into a scaled output range scale_min to scale_max?

easy

A. scaled = (raw - raw_min) * (scale_max - scale_min) / (raw_max - raw_min) + scale_min

B. scaled = raw * (scale_max - scale_min) / (raw_max + raw_min) + scale_min

C. scaled = (raw + raw_min) * (scale_max + scale_min) / (raw_max - raw_min)

D. scaled = (raw - raw_max) * (scale_min - scale_max) / (raw_min - raw_max) + scale_max

Solution

1. Step 1: Recall the scaling formula

   The formula maps raw input linearly to the scaled range using subtraction and division.

2. Step 2: Check each formula

   scaled = (raw - raw_min) * (scale_max - scale_min) / (raw_max - raw_min) + scale_min correctly subtracts raw_min, scales by ratio of output to input range, then adds scale_min.

3. Final Answer:

   scaled = (raw - raw_min) * (scale_max - scale_min) / (raw_max - raw_min) + scale_min -> Option A

4. Quick Check:

   Scaling formula = scaled = (raw - raw_min) * (scale_max - scale_min) / (raw_max - raw_min) + scale_min [OK]

Hint: Use (raw - raw_min) * output_range / input_range + scale_min [OK]

Common Mistakes:

• Adding raw_min instead of subtracting
• Using addition instead of subtraction in denominator
• Mixing max and min values incorrectly

3. Given a raw input value of 2500 from a sensor with raw range 0-4095, scaled to temperature range 0-100°C using the formula scaled = (raw - 0) * (100 - 0) / (4095 - 0) + 0, what is the scaled temperature?

medium

A. 61.07°C

B. 25.00°C

C. 100.00°C

D. 0.61°C

Solution

1. Step 1: Substitute values into formula

   scaled = (2500 - 0) * (100 - 0) / (4095 - 0) + 0 = 2500 * 100 / 4095

2. Step 2: Calculate the scaled value

   scaled = 250000 / 4095 ≈ 61.07°C

3. Final Answer:

   61.07°C -> Option A

4. Quick Check:

   2500/4095 ≈ 0.61 * 100 = 61.07 [OK]

Hint: Divide raw by max raw, multiply by max scale [OK]

Common Mistakes:

• Using raw_max as 2500 instead of 4095
• Forgetting to subtract raw_min
• Mixing up numerator and denominator

4. A PLC program uses this scaling code snippet:

scaled = (raw - 100) * (200 - 0) / (1000 - 0) + 0

What is the error in this scaling formula?

medium

A. The raw_min value should be 0, not 100

B. The denominator should be (1000 - 100) instead of (1000 - 0)

C. The formula should subtract scale_min, not raw_min

D. The scale_max value should be 100, not 200

Solution

1. Step 1: Identify raw input range

   Raw input minimum is 100, maximum is 1000, so input range is 1000 - 100 = 900.

2. Step 2: Check denominator in formula

   The formula uses (1000 - 0) = 1000, which is incorrect; it should be (1000 - 100) = 900.

3. Final Answer:

   The denominator should be (1000 - 100) instead of (1000 - 0) -> Option B

4. Quick Check:

   Input range = max - min = 900, not 1000 [OK]

Hint: Denominator = raw_max - raw_min, not raw_max - 0 [OK]

Common Mistakes:

• Using wrong input range denominator
• Confusing scale and raw min/max
• Subtracting scale_min instead of adding

5. You have a sensor outputting raw values from 500 to 3500 representing pressure from 20 to 100 psi. Which formula correctly scales a raw input raw to pressure?

hard

A. pressure = (raw - 500) * (100 - 20) / (3500 - 500) + 0

B. pressure = (raw - 0) * (100 - 20) / (3500 - 500) + 20

C. pressure = (raw - 500) * (100 - 20) / (3500 - 0) + 20

D. pressure = (raw - 500) * (100 - 20) / (3500 - 500) + 20

Solution

1. Step 1: Identify raw and scale ranges

   Raw range: 500 to 3500; pressure range: 20 to 100 psi.

2. Step 2: Apply scaling formula

   Use (raw - raw_min) * (scale_max - scale_min) / (raw_max - raw_min) + scale_min.

3. Step 3: Check each option

   pressure = (raw - 500) * (100 - 20) / (3500 - 500) + 20 correctly uses raw_min=500, raw_max=3500, scale_min=20, scale_max=100.

4. Final Answer:

   pressure = (raw - 500) * (100 - 20) / (3500 - 500) + 20 -> Option D

5. Quick Check:

   Correct raw and scale min/max used in formula [OK]

Hint: Always subtract raw_min and add scale_min in formula [OK]

Common Mistakes:

• Using 0 instead of raw_min in subtraction
• Adding 0 instead of scale_min at end
• Mixing raw_max with 0 in denominator