Operator precedence in C++ - Step-by-Step Execution

Concept Flow - Operator precedence

Start Expression

↓

Identify Operators

↓

Check Precedence Levels

↓

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 operators in an expression by following their precedence order, starting with the highest precedence operators first, then moving to lower ones until the expression is fully evaluated.

Execution Sample

C++

int result = 3 + 4 * 2;
std::cout << result << std::endl;

Calculates the expression 3 + 4 * 2, showing how multiplication happens before addition.

Execution Table

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

💡 All operators evaluated according to precedence, final result is 11

Variable Tracker

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

Key Moments - 2 Insights

Why does multiplication happen before addition in the expression?

Because multiplication has higher precedence than addition, as shown in step 1 of the execution_table where 4 * 2 is evaluated before adding 3.

What if we want addition to happen first?

We can use parentheses to change precedence, for example (3 + 4) * 2 would evaluate addition first.

Visual Quiz - 3 Questions

Look at the execution_table, what is the result after step 1?

A 11

B 8

C 3

D Undefined

💡 Hint

Check the 'Result' column in row for step 1 in execution_table

At which step is the addition operator evaluated?

A Step 2

B Step 3

C Step 1

D Never

💡 Hint

Look at the 'Operator Evaluated' column in execution_table

If the expression was (3 + 4) * 2, what would be the result after the first step?

A 8

B 11

C 7

D 14

💡 Hint

Parentheses change precedence, so addition happens first

Concept Snapshot

Operator precedence determines the order in which parts of an expression are calculated.
Higher precedence operators (like *) are evaluated before lower ones (like +).
Use parentheses () to override default precedence.
Without parentheses, expressions are evaluated left to right respecting precedence.
Example: 3 + 4 * 2 equals 3 + (4 * 2) = 11.

Full Transcript

This visual execution shows how operator precedence works in C++. The expression '3 + 4 * 2' is evaluated step-by-step. First, multiplication (*) is done because it has higher precedence than addition (+). So, 4 * 2 equals 8. Then, addition is done: 3 + 8 equals 11. The final result stored in 'result' is 11. If you want addition first, use parentheses like (3 + 4) * 2. This changes the order and result. Understanding operator precedence helps avoid mistakes in calculations.

Practice

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

easy

A. Addition (+)

B. Subtraction (-)

C. Multiplication (*)

D. Division (/)

Solution

1. Step 1: Identify operators in the expression

   The expression has addition (+) and multiplication (*).

2. Step 2: Recall operator precedence rules

   Multiplication (*) has higher precedence than addition (+), so it is evaluated first.

3. Final Answer:

   Multiplication (*) -> Option C

4. Quick Check:

   Multiplication before addition = Multiplication (*) [OK]

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

Common Mistakes:

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

2. Which of the following expressions is syntactically correct in C++?

easy

A. int x = 5 + (3 * 2);

B. int x = 5 + 3 *;

C. int x = 5 + *3;

D. int x = 5 + 3 * 2);

Solution

1. Step 1: Check each expression for syntax errors

   int x = 5 + *3; has an invalid use of * before 3. int x = 5 + 3 *; ends with * which is incomplete. int x = 5 + 3 * 2); has an unmatched closing parenthesis.

2. Step 2: Confirm correct syntax

   int x = 5 + (3 * 2); uses parentheses correctly and has valid operators and operands.

3. Final Answer:

   int x = 5 + (3 * 2); -> Option A

4. Quick Check:

   Valid syntax with parentheses and operators = int x = 5 + (3 * 2); [OK]

Hint: Check for balanced parentheses and proper operator placement [OK]

Common Mistakes:

• Misplacing operators without operands
• Unbalanced parentheses
• Using operators incorrectly

3. What is the output of the following code?

int a = 2, b = 3, c = 4;
int result = a + b * c / a - b;
std::cout << result;

medium

A. 5

B. 2

C. 4

D. 3

Solution

1. Step 1: Evaluate multiplication and division first

   b * c = 3 * 4 = 12; then 12 / a = 12 / 2 = 6.

2. Step 2: Evaluate addition and subtraction left to right

   a + 6 = 2 + 6 = 8; then 8 - b = 8 - 3 = 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Multiplication/division before addition/subtraction = 5 [OK]

Hint: Do * and / before + and -, left to right [OK]

Common Mistakes:

• Adding before multiplying
• Ignoring division precedence
• Calculating subtraction before addition

4. Find the error in the following code snippet:

int x = 10;
int y = 5;
int z = x + y * / 2;
std::cout << z;

medium

A. Division by zero error

B. Syntax error due to misplaced operator

C. Logical error in calculation

D. No error, code runs fine

Solution

1. Step 1: Analyze the expression for syntax correctness

   The expression x + y * / 2 has two operators (*) and (/) together without an operand, which is invalid syntax.

2. Step 2: Confirm the error type

   This causes a syntax error because the compiler cannot parse the expression correctly.

3. Final Answer:

   Syntax error due to misplaced operator -> Option B

4. Quick Check:

   Invalid operator sequence causes syntax error [OK]

Hint: Check operator placement for missing operands [OK]

Common Mistakes:

• Assuming code runs despite syntax errors
• Confusing syntax error with runtime error
• Ignoring operator adjacency rules

5. Consider the expression int result = 10 - 3 * 2 + 4 / 2;. How can you change it using parentheses to make addition happen before multiplication and division?

hard

A. int result = 10 - ((3 * 2) + 4) / 2;

B. int result = ((10 - 3) * 2 + 4) / 2;

C. int result = 10 - ((3 * 2) + (4 / 2));

D. int result = 10 - (3 * (2 + 4)) / 2;

Solution

1. Step 1: Understand original precedence

   Original expression evaluates multiplication and division before addition and subtraction.

2. Step 2: Use parentheses to force addition before multiplication/division

   int result = 10 - (3 * (2 + 4)) / 2; groups (2 + 4) first, so addition happens before multiplication and division.

3. Final Answer:

   int result = 10 - (3 * (2 + 4)) / 2; -> Option D

4. Quick Check:

   Parentheses change order to add before multiply/divide [OK]

Hint: Use parentheses to group additions before other ops [OK]

Common Mistakes:

• Misplacing parentheses changing meaning
• Not grouping addition properly
• Assuming left-to-right overrides precedence