Operator precedence - Step-by-Step Execution

Concept Flow - Operator precedence

Start Expression

↓

Identify Operators

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Check Precedence Levels

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Evaluate Highest Precedence Operator

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Replace with Result

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Repeat Until Expression Fully Evaluated

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Final Result

The program evaluates expressions by first identifying operators, then applying them in order of their precedence from highest to lowest until the expression is fully calculated.

Execution Sample

C

int result = 3 + 4 * 2;
printf("%d", result);

Calculates the expression 3 + 4 * 2 considering operator precedence and prints the result.

Execution Table

Step	Expression	Operator Evaluated	Operation	Resulting Expression
1	3 + 4 * 2	*	4 * 2 = 8	3 + 8
2	3 + 8	+	3 + 8 = 11	11
3	11	None	Expression fully evaluated	11

💡 No more operators left; final result is 11

Variable Tracker

Variable	Start	After Step 1	After Step 2	Final
result	undefined	undefined	11	11

Key Moments - 2 Insights

Why is multiplication done before addition in the expression?

Because multiplication (*) has higher precedence than addition (+), so it is evaluated first as shown in step 1 of the execution table.

What happens if we ignore operator precedence and evaluate left to right?

If evaluated left to right ignoring precedence, 3 + 4 would be 7, then 7 * 2 = 14, which is incorrect. The execution table shows correct precedence evaluation.

Visual Quiz - 3 Questions

Look at the execution table, what is the expression after step 1?

A 3 + 8

B 7 * 2

C 11

D 3 + 4 * 2

💡 Hint

Check the 'Resulting Expression' column in step 1 of the execution table.

At which step is the addition operator evaluated?

A Step 1

B Step 2

C Step 3

D Never

💡 Hint

Look at the 'Operator Evaluated' column to find when '+' is processed.

If the expression was 3 * 4 + 2, what would be the final result?

A 11

B 20

C 14

D Undefined

💡 Hint

Multiply first (3*4=12), then add 2, similar to the execution flow shown.

Concept Snapshot

Operator precedence determines the order in which parts of an expression are evaluated.
Higher precedence operators (like *) are evaluated before lower ones (like +).
Expressions are evaluated step-by-step from highest to lowest precedence.
Ignoring precedence can lead to wrong results.
Use parentheses to change evaluation order explicitly.

Full Transcript

This visual execution shows how operator precedence works in C. The expression 3 + 4 * 2 is evaluated by first calculating 4 * 2 because multiplication has higher precedence than addition. This results in 8, then 3 + 8 is evaluated to 11. The execution table tracks each step, showing which operator is evaluated and the resulting expression. Variables update accordingly, with 'result' holding the final value 11. Key moments clarify why multiplication happens before addition and what would happen if precedence was ignored. The quiz tests understanding by asking about intermediate expressions and evaluation steps. Remember, operator precedence ensures expressions are calculated correctly and predictably.

Practice

1. Which operator has the highest precedence in the expression 3 + 4 * 5?

easy

A. Division (/)

B. Addition (+)

C. Subtraction (-)

D. Multiplication (*)

Solution

1. Step 1: Recall operator precedence rules

   Multiplication and division have higher precedence than addition and subtraction in C.

2. Step 2: Identify operators in the expression

   The expression has addition (+) and multiplication (*). Multiplication runs first.

3. Final Answer:

   Multiplication (*) -> Option D

4. Quick Check:

   Multiplication > Addition [OK]

Hint: Multiplication and division run before addition and subtraction [OK]

Common Mistakes:

• Thinking addition runs before multiplication
• Ignoring operator precedence
• Assuming left to right always applies

2. Which of the following expressions is correctly written to add 2 and 3, then multiply the result by 4?

easy

A. (2 + 3) * 4

B. 2 + (3 * 4)

C. 2 + 3 * 4

D. 2 * 3 + 4

Solution

1. Step 1: Understand the desired calculation

   Add 2 and 3 first, then multiply by 4.

2. Step 2: Check parentheses usage

   Only (2 + 3) * 4 uses parentheses to add 2 and 3 first, then multiply by 4.

3. Final Answer:

   (2 + 3) * 4 -> Option A

4. Quick Check:

   Parentheses change order to add first [OK]

Hint: Use parentheses to force addition before multiplication [OK]

Common Mistakes:

• Ignoring parentheses and trusting default precedence
• Misreading the expression order
• Assuming left to right overrides precedence

3. What is the output of this C code?

int x = 5 + 3 * 2 - 4 / 2;
printf("%d", x);

medium

A. 10

B. 9

C. 11

D. 8

Solution

1. Step 1: Apply operator precedence

   Multiplication and division first: 3 * 2 = 6, 4 / 2 = 2.

2. Step 2: Calculate the expression left to right

   Expression becomes 5 + 6 - 2 = 9.

3. Final Answer:

   9 -> Option B

4. Quick Check:

   5 + 6 - 2 = 9 [OK]

Hint: Calculate * and / before + and - [OK]

Common Mistakes:

• Adding before multiplying
• Dividing after subtraction
• Calculating left to right ignoring precedence

4. Identify the error in this expression:

int result = 10 / 2 * 3 + 4 - 5;

medium

A. Multiplication and division have the same precedence and are left to right

B. Subtraction should be done before multiplication

C. Addition has higher precedence than multiplication

D. Division should be done after addition

Solution

1. Step 1: Check operator precedence and associativity

   Multiplication (*) and division (/) have the same precedence and are evaluated left to right.

2. Step 2: Verify the expression evaluation order

   Expression evaluates as ((10 / 2) * 3) + 4 - 5, which is correct.

3. Final Answer:

   Multiplication and division have the same precedence and are left to right -> Option A

4. Quick Check:

   * and / same precedence, left to right [OK]

Hint: Remember * and / are equal precedence, evaluated left to right [OK]

Common Mistakes:

• Thinking division happens after addition
• Assuming addition has higher precedence
• Ignoring left-to-right rule for same precedence

5. Given the expression int y = 8 - 3 + 2 * 4 / 2;, which parentheses placement changes the result to 14?

hard

A. 8 - 3 + (2 * 4) / 2

B. 8 - (3 + 2) * 4 / 2

C. (8 - 3 + 2) * 4 / 2

D. (8 - (3 + 2)) * 4 / 2

Solution

1. Step 1: Calculate original expression

   * and / first left-to-right: 2 * 4 = 8, 8 / 2 = 4; then 8 - 3 + 4 = 9.

2. Step 2: Evaluate (8 - 3 + 2) * 4 / 2

   (8 - 3 + 2) = 7, 7 * 4 = 28, 28 / 2 = 14.

3. Step 3: Confirm others

   8 - (3 + 2) * 4 / 2 = 8 - 20 / 2 = 8 - 10 = -2; 8 - 3 + (2 * 4) / 2 = 9; (8 - (3 + 2)) * 4 / 2 = 3 * 4 / 2 = 6.

4. Final Answer:

   (8 - 3 + 2) * 4 / 2 -> Option C

5. Quick Check:

   Parentheses force addition before multiplication [OK]

Hint: Try parentheses around addition to change multiplication order [OK]

Common Mistakes:

• Assuming original order always applies
• Not recalculating expression after adding parentheses
• Misplacing parentheses without recalculating