Question

What is the output of the following statements? Suppose a and b are int variables, \(c\) is a double variable, and \(a=13, b=5,\) and \(c=17.5\) a. cout << a + b – c << endl; b. cout << 15 / 2 + c << endl; c. cout << a / static_cast(b) + 2 * c << endl; d. cout << 14 % 3 + 6.3 + b / a << endl; e. cout << static_cast(c) % 5 + a – b << endl; f. cout << 13.5 / 2 + 4.0 * 3.5 + 18 << endl;

Short answer

The outputs are 0.5, 24.5, 37.6, ~8.6846, 10, 38.75.

Step-by-step solution

Evaluate Expression a

Calculate the expression in statement (a): Expression: \( a + b - c \).Substitute the values: \( 13 + 5 - 17.5 \).Perform the operations: \( 18 - 17.5 = 0.5 \).Therefore, the output is 0.5.

Evaluate Expression b

Calculate the expression in statement (b): Expression: \( 15 / 2 + c \).Integer division of 15 by 2 yields 7 (since it's int division).Substitute the values into the expression: \( 7 + 17.5 \).Perform the addition: \( 7 + 17.5 = 24.5 \).Thus, the output is 24.5.

Evaluate Expression c

Calculate the expression in statement (c): Expression: \( a / (b \text{ cast to double}) + 2 * c \).Substitute and convert the values: \( 13 / 5.0 + 2 * 17.5 \).Perform the division: \( 2.6 + 35.0 \).Add the numbers: \( 2.6 + 35.0 = 37.6 \).Therefore, the output is 37.6.

Evaluate Expression d

Calculate the expression in statement (d): Expression: \( 14 \% 3 + 6.3 + b / a \).Calculate 14 modulo 3: the remainder is 2.Perform the division: \( 5 / 13 \) which approximates to \( 0.3846 \).Substitute these into the expression: \( 2 + 6.3 + 0.3846 \).Add the numbers: \( 8.6846 \) (approximated as 8.6846 for precision)So, the output is approximately 8.6846.

Evaluate Expression e

Calculate the expression in statement (e): Expression: \( \text{static_cast(c)} \% 5 + a - b \).Convert \( c \) to an int: 17. Divide 17 by 5 yields a remainder of 2.Substitute these into the expression: \( 2 + 13 - 5 \).Perform the operations: \( 15 - 5 = 10 \).Thus, the output is 10.

Evaluate Expression f

Calculate the expression in statement (f): Expression: \( 13.5 / 2 + 4.0 * 3.5 + 18 \).Perform the division: \( 6.75 \).Calculate \( 4.0 * 3.5 = 14.0 \).Sum: \( 6.75 + 14.0 + 18 \).Add the numbers: \( 38.75 \).Hence, the output is 38.75.

Key concepts

Integer Division

In C++, when you divide two integers, the result is also an integer. This is known as integer division. It means any fractional part of the division result is discarded. For instance, consider expression b in the exercise:

• Expression: \( 15 / 2 \)
• Result: Because both 15 and 2 are integers, dividing them gives 7, not 7.5.
• Follow-up calculation involves adding this integer result to a double: \( 7 + 17.5 \).
• Final output: 24.5

Keep in mind that integer division can lead to loss of precision if one of the numbers used in division is converted to a double unintentionally. Therefore, it's important to understand when integer division is taking place to avoid unexpected results.

Type Casting in C++

Type casting in C++ allows you to convert a variable from one data type to another explicitly. This process is essential when working with arithmetic operations involving different data types. In statement c of the problem:

• Expression: \( a / \text{static_cast(b)} + 2 * c \)
• Here, we use \( \text{static_cast(b)} \) to convert integer \( b \) into a double.
• Doing so ensures that \( a / b \) is calculated as a floating-point division, not an integer division, giving \( 2.6 \).

Type casting is helpful when you need your calculations to include decimal places. Always use the most appropriate type to avoid losing data precision.

Modulo Operation

The modulo operation gives the remainder of a division between integers. In the exercise, this is seen in expression d and e with the usages:

• For statement d: \( 14 \% 3 \)
• Result: The remainder when 14 is divided by 3 is 2.
• For statement e: \( \text{static_cast(c)} \% 5 \)
• After converting the double \( c \) to integer 17, the remainder when 17 is divided by 5 is also 2.

The modulo operation can be particularly useful for tasks like checking for even or odd numbers, looping over an array circularly, or hashing functions.

Expression Evaluation

Evaluating expressions involves following the precedence rules of arithmetic operations. These rules dictate the order in which multiple operations in an expression are carried out:

• Use PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right).
• In the various statements, calculations must be performed in this order for accurate results.
• For example, in statement f: \( 13.5 / 2 + 4.0 * 3.5 + 18 \)
• Perform \( 13.5 / 2 = 6.75 \)
• Then \( 4.0 * 3.5 = 14.0 \)
• Finally, add the results: \( 6.75 + 14.0 + 18 = 38.75 \)

This sequence of operations ensures that each part of an expression is calculated in the proper order, yielding the correct result. Understanding these rules will aid greatly in minimizing errors in your calculations.