Question

(Order of Evalution) State the order of evaluation of the operators in each of the following C++ statements and show the value of x after each statement is performed. a) x = 7 + 3 * 6 / 2 - 1; b) x = 2 % 2 + 2 * 2 - 2 / 2; c) x = ( 3 * 9 * ( 3 + ( 9 * 3 / ( 3 ) ) ) );

Short answer

a) x = 15, b) x = 3, c) x = 324.

Step-by-step solution

Evaluate the first expression

First, apply the order of operations: multiplication and division from left to right, then addition and subtraction from left to right.For a) x = 7 + 3 * 6 / 2 - 1;1. 3 * 6 = 18,2. 18 / 2 = 9,3. 7 + 9 = 16,4. 16 - 1 = 15.Therefore, x is evaluated to 15.

Evaluate the second expression

Again, apply the order of operations: modulus, multiplication and division, then addition and subtraction.For b) x = 2 % 2 + 2 * 2 - 2 / 2;1. 2 % 2 = 0,2. 2 * 2 = 4,3. 2 / 2 = 1,4. 0 + 4 = 4,5. 4 - 1 = 3.Thus, x is evaluated to 3.

Evaluate the third expression

For c) x = ( 3 * 9 * ( 3 + ( 9 * 3 / ( 3 ) ) ) );Use the order of operations, starting with the innermost parentheses:1. 9 * 3 = 27,2. 27 / 3 = 9,3. 3 + 9 = 12,4. 3 * 9 = 27,5. 27 * 12 = 324.Hence, x is evaluated to 324.

Key concepts

C++ Arithmetic Operations

Understanding C++ arithmetic operations is crucial for performing basic calculations within your code. These include addition (+), subtraction (-), multiplication (*), division (/), and modulus (%). Each of these operations is essential for manipulating numbers, and they are the building blocks of more complex expressions.

Take the expression x = 7 + 3 * 6 / 2 - 1; as an example. We perform multiple arithmetic operations here to determine the value of x. The operations are carried out based on their precedence, which is inherently understood by the C++ compiler. For instance, multiplication and division take precedence over addition and subtraction, which affects the order in which these operations are performed. It's like a mathematical ballet where each operation waits for its turn to take the stage.

In our everyday math, we might group certain numbers with parentheses to indicate they should be calculated first; C++ uses the same logic with arithmetic operations, only it also has built-in rules (the precedence) to decide which calculations are done first in their absence.

• + and - add and subtract numbers respectively.
• * and / multiply and divide numbers respectively.
• The modulus (%) operator returns the remainder of a division.

These fundamental operations combined form the expressions you will work with when programming in C++.

Operator Precedence

The concept of Operator precedence tells the C++ compiler which operations to perform first in an expression. It's like a hierarchy of operations where specific types of operations take priority over others. For example, in the expression x = 7 + 3 * 6 / 2 - 1;, multiplication and division have higher precedence than addition and subtraction.

Here's a simplified order of precedence from highest to lowest:

1. Parentheses ()
2. Multiplication *, Division /, and Modulus %
3. Addition + and Subtraction -

When faced with operators of the same precedence, such as * and /, C++ evaluates them from left to right. It's important to grasp this concept thoroughly since misunderstanding operator precedence can lead to unexpected results in your programs. Whenever there's potential confusion, or when you want to explicitly state your intent, wrapping parts of your expression in parentheses can clarify the order of operations, ensuring the outcome is as intended.

Always recalling the mantra 'Please Excuse My Dear Aunt Sally' (PEMDAS) from math class can be helpful when considering operator precedence. Although not all characters correspond directly to C++ operations, the order is comparatively consistent: Parentheses first, then Exponents (in C++, using functions like pow() for power operations), followed by Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). C++ respects this hierarchy, ensuring mathematical expressions compute correctly.

Expression Evaluation

The process of Expression evaluation is where C++ follows the established operator precedence rules to produce a single value from an expression. It's like following a recipe where the instructions are your operators, and the ingredients are your operands. When you evaluate an expression such as x = 2 % 2 + 2 * 2 - 2 / 2;, you're directing C++ to combine these 'ingredients' in a specific 'order of operations' to cook up the final value of x.

Remember to be aware of the operator precedence rules in complex expressions to ensure you understand how the expression is being evaluated by the C++ compiler. For example, consider the exercise statement x = ( 3 * 9 * ( 3 + ( 9 * 3 / ( 3 ) ) ) );. C++ will first evaluate the most deeply nested expression and work its way outwards, respecting the operator precedence as it goes. It's also vital to pay attention to integer division where numbers are integers. Since C++ performs integer division, the result is truncated to an integer. This could lead to unexpected results if not properly anticipated.

Understanding expression evaluation will help prevent bugs and logical errors in your code. It's akin to ensuring that the sequence of steps in the recipe is followed to the letter to achieve the perfect dish. Such meticulousness in following the correct expression evaluation process will serve you well in C++ programming.