Comparison instructions (EQ, NE, GT, LT) in PLC Programming - Time & Space Complexity

Time Complexity: Comparison instructions (EQ, NE, GT, LT)

O(n)

Understanding Time Complexity

We want to understand how the time to run comparison instructions changes as we use them more in a program.

Specifically, how does running EQ, NE, GT, or LT instructions affect execution time when repeated?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Example: Check array values against a threshold
FOR i := 0 TO n - 1 DO
  IF array[i] > threshold THEN
    output[i] := TRUE;
  ELSE
    output[i] := FALSE;
  END_IF;
END_FOR;
    

This code compares each element in an array to a threshold using the GT (greater than) instruction.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The GT comparison inside the loop.
• How many times: Exactly once for each element in the array, so n times.

How Execution Grows With Input

Each new element adds one more comparison operation.

Input Size (n)	Approx. Operations
10	10 comparisons
100	100 comparisons
1000	1000 comparisons

Pattern observation: The number of comparisons grows directly with the number of elements.

Final Time Complexity

Time Complexity: O(n)

This means the time to run these comparison instructions grows in a straight line as the input size grows.

Common Mistake

[X] Wrong: "Comparison instructions take constant time no matter how many times they run, so the whole loop is constant time."

[OK] Correct: Each comparison runs once per element, so more elements mean more comparisons and more time.

Interview Connect

Understanding how simple comparisons add up helps you explain how programs handle data step-by-step, a key skill in automation and control programming.

Self-Check

"What if we added a nested loop that compares every element to every other element? How would the time complexity change?"

Practice

1. Which comparison instruction checks if two values are exactly the same in PLC programming?

easy

A. EQ

B. NE

C. GT

D. LT

Solution

1. Step 1: Understand the meaning of EQ

   EQ stands for 'equal' and checks if two values are exactly the same.

2. Step 2: Compare with other instructions

   NE means not equal, GT means greater than, and LT means less than, so they do not check equality.

3. Final Answer:

   EQ -> Option A

4. Quick Check:

   EQ means equal [OK]

Hint: EQ means equal, so it checks if values match exactly [OK]

Common Mistakes:

• Confusing EQ with NE
• Thinking GT checks equality
• Mixing LT with EQ

2. Which of the following is the correct syntax to check if variable A is greater than variable B in a PLC program?

easy

A. IF A LT B THEN

B. IF A NE B THEN

C. IF A EQ B THEN

D. IF A GT B THEN

Solution

1. Step 1: Identify the comparison for 'greater than'

   GT means 'greater than', so to check if A is greater than B, use 'A GT B'.

2. Step 2: Check other options

   LT means less than, EQ means equal, NE means not equal, so they are incorrect for this check.

3. Final Answer:

   IF A GT B THEN -> Option D

4. Quick Check:

   GT means greater than [OK]

Hint: GT means greater than, so use it to compare if A > B [OK]

Common Mistakes:

• Using LT instead of GT
• Confusing EQ with GT
• Using NE for greater than check

3. Given the following PLC code snippet:

VAR
  X: INT := 5;
  Y: INT := 10;
  Result: BOOL;
END_VAR

Result := X LT Y;

What will be the value of Result after execution?

medium

A. Syntax Error

B. FALSE

C. TRUE

D. Undefined

Solution

1. Step 1: Understand the comparison LT

   LT means 'less than'. The code checks if X (5) is less than Y (10).

2. Step 2: Evaluate the condition

   Since 5 is less than 10, the condition is true, so Result will be TRUE.

3. Final Answer:

   TRUE -> Option C

4. Quick Check:

   5 LT 10 = TRUE [OK]

Hint: LT means less than; 5 < 10 is true [OK]

Common Mistakes:

• Thinking LT means greater than
• Assuming Result is FALSE
• Confusing syntax with error

4. Identify the error in this PLC comparison instruction:

IF A NEQ B THEN
  // do something
END_IF

medium

A. Missing THEN keyword

B. NEQ is not a valid comparison instruction

C. Comparison should be EQ instead of NEQ

D. IF statement missing parentheses

Solution

1. Step 1: Check the comparison instruction used

   The code uses 'NEQ' which is not a standard PLC comparison instruction.

2. Step 2: Identify correct instruction

   The correct instruction for 'not equal' is 'NE', not 'NEQ'.

3. Final Answer:

   NEQ is not a valid comparison instruction -> Option B

4. Quick Check:

   Use NE for not equal, not NEQ [OK]

Hint: Use NE for not equal, not NEQ [OK]

Common Mistakes:

• Using NEQ instead of NE
• Forgetting THEN keyword
• Adding unnecessary parentheses

5. You want to write a PLC program that turns on a motor only if the temperature is greater than 50 and the pressure is less than 100. Which combination of comparison instructions correctly checks this condition?

hard

A. IF Temperature GT 50 AND Pressure LT 100 THEN Motor := TRUE;

B. IF Temperature LT 50 OR Pressure GT 100 THEN Motor := TRUE;

C. IF Temperature EQ 50 AND Pressure EQ 100 THEN Motor := TRUE;

D. IF Temperature NE 50 AND Pressure NE 100 THEN Motor := TRUE;

Solution

1. Step 1: Translate the condition into comparisons

   The motor should turn on if temperature is greater than 50 (GT 50) and pressure is less than 100 (LT 100).

2. Step 2: Check each option

   IF Temperature GT 50 AND Pressure LT 100 THEN Motor := TRUE; uses GT and LT with AND, matching the condition exactly. Other options use wrong comparisons or OR instead of AND.

3. Final Answer:

   IF Temperature GT 50 AND Pressure LT 100 THEN Motor := TRUE; -> Option A

4. Quick Check:

   GT and LT with AND matches condition [OK]

Hint: Use GT for greater, LT for less, combine with AND for both conditions [OK]

Common Mistakes:

• Using OR instead of AND
• Using EQ instead of GT or LT
• Mixing NE with equality checks