4.x — Chapter 4 summary and quiz

Chapter Review

The smallest unit of memory is a binary digit, also called a bit. The smallest unit amount of memory that can be addressed (accessed) directly is a byte. The modern standard is that a byte equals 8 bits.

A data type tells the compiler how to interpret the contents of memory in some meaningful way.

C++ comes with support for many fundamental data types, including floating point numbers, integers, boolean, chars, null pointers, and void.

Void is used to indicate no type. It is primarily used to indicate that a function does not return a value.

Different types take different amounts of memory, and the amount of memory used may vary by machine.

The sizeof operator can be used to return the size of a type in bytes.

Signed integers are used for holding positive and negative whole numbers, including 0. The set of values that a specific data type can hold is called its range. When using integers, keep an eye out for overflow and integer division problems.

Unsigned integers only hold positive numbers (and 0), and should generally be avoided unless you’re doing bit-level manipulation.

Fixed-width integers are integers with guaranteed sizes, but they may not exist on all architectures. The fast and least integers are the fastest and smallest integers that are at least some size. std::int8_t and std::uint8_t should generally be avoided, as they tend to behave like chars instead of integers.

size_t is an unsigned integral type that is used to represent the size or length of objects.

Scientific notation is a shorthand way of writing lengthy numbers. C++ supports scientific notation in conjunction with floating point numbers. The digits in the significand (the part before the e) are called the significant digits.

Floating point is a set of types designed to hold real numbers (including those with a fractional component). The precision of a number defines how many significant digits it can represent without information loss. A rounding error can occur when too many significant digits are stored in a floating point number that can’t hold that much precision. Rounding errors happen all the time, even with simple numbers such as 0.1. Because of this, you shouldn’t compare floating point numbers directly.

The Boolean type is used to store a true or false value.

If statements allow us to execute one or more lines of code if some condition is true. The conditional expression of an if-statement is interpreted as a boolean value. An else statement can be used to execute a statement when a prior if-statement condition evaluates to false.

Char is used to store values that are interpreted as an ASCII character. When using chars, be careful not to mix up ASCII code values and numbers. Printing a char as an integer value requires use of static_cast.

Angled brackets are typically used in C++ to represent something that needs a parameterizable type. This is used with static_cast to determine what data type the argument should be converted to (e.g. static_cast<int>(x) will return the value of x as an int).

Quiz time

Question #1

Pick the appropriate data type for a variable in each of the following situations. Be as specific as possible. If the answer is an integer, pick int (if size isn’t important), or a specific fixed-width integer type (e.g. std::int16_t) based on range.

a) The age of the user (in years) (assume the size of the type isn’t important)

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b) Whether the user wants the application to check for updates

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c) pi (3.14159265)

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d) The number of pages in a textbook (assume size is not important)

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e) The length of a couch in feet, to 2 decimal places (assume size is important)

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f) How many times you’ve blinked since you were born (note: answer is in the millions)

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g) A user selecting an option from a menu by letter

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h) The year someone was born (assuming size is important)

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Question #2

Write the following program: The user is asked to enter 2 floating point numbers (use doubles). The user is then asked to enter one of the following mathematical symbols: +, -, *, or /. The program computes the answer on the two numbers the user entered and prints the results. If the user enters an invalid symbol, the program should print nothing.

Example of program:

Enter a double value: 6.2
Enter a double value: 5
Enter +, -, *, or /: *
6.2 * 5 is 31

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#include <iostream>

double getDouble()
{
    std::cout << "Enter a double value: ";
    double x{};
    std::cin >> x;
    return x;
}

char getOperator()
{
    std::cout << "Enter +, -, *, or /: ";
    char operation{};
    std::cin >> operation;
    return operation;
}

void printResult(double x, char operation, double y)
{
    if (operation == '+')
        std::cout << x << " + " << y << " is " << x + y << '\n';
    else if (operation == '-')
        std::cout << x << " - " << y << " is " << x - y << '\n';
    else if (operation == '*')
        std::cout << x << " * " << y << " is " << x * y << '\n';
    else if (operation == '/')
        std::cout << x << " / " << y << " is " << x / y << '\n';
}

int main()
{
    double x { getDouble() };
    double y { getDouble() };

    char operation { getOperator() };

    printResult(x, operation, y);

    return 0;
}

Question #3

Extra credit: This one is a little more challenging.

Write a short program to simulate a ball being dropped off of a tower. To start, the user should be asked for the height of the tower in meters. Assume normal gravity (9.8 m/s²), and that the ball has no initial velocity (the ball is not moving to start). Have the program output the height of the ball above the ground after 0, 1, 2, 3, 4, and 5 seconds. The ball should not go underneath the ground (height 0).

Use a function to calculate the height of the ball after x seconds. The function can calculate how far the ball has fallen after x seconds using the following formula: distance fallen = gravity_constant * x_seconds² / 2

Expected output:

Enter the height of the tower in meters: 100
At 0 seconds, the ball is at height: 100 meters
At 1 seconds, the ball is at height: 95.1 meters
At 2 seconds, the ball is at height: 80.4 meters
At 3 seconds, the ball is at height: 55.9 meters
At 4 seconds, the ball is at height: 21.6 meters
At 5 seconds, the ball is on the ground.

Note: Depending on the height of the tower, the ball may not reach the ground in 5 seconds -- that’s okay. We’ll improve this program once we’ve covered loops.
Note: The ^ symbol isn’t an exponent in C++. Implement the formula using multiplication instead of exponentiation.
Note: Remember to use double literals for doubles, e.g. 2.0 rather than 2.

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#include <iostream>

// Gets tower height from user and returns it
double getTowerHeight()
{
	std::cout << "Enter the height of the tower in meters: ";
	double towerHeight{};
	std::cin >> towerHeight;
	return towerHeight;
}

// Returns the current ball height after "seconds" seconds
double calculateBallHeight(double towerHeight, int seconds)
{
	double gravity { 9.8 };
    
	// Using formula: s = (u * t) + (a * t^2) / 2
	// here u (initial velocity) = 0, so (u * t) = 0
	double fallDistance { gravity * (seconds * seconds) / 2.0 };
	double ballHeight { towerHeight - fallDistance };

	// If the ball would be under the ground, place it on the ground
	if (ballHeight < 0.0)
		return 0.0;
    
	return ballHeight;
}

// Prints ball height above ground
void printBallHeight(double ballHeight, int seconds)
{
	if (ballHeight > 0.0)
		std::cout << "At " << seconds << " seconds, the ball is at height: " << ballHeight << " meters\n";
	else
		std::cout << "At " << seconds << " seconds, the ball is on the ground.\n";
}

// Calculates the current ball height and then prints it
// This is a helper function to make it easier to do this
void calculateAndPrintBallHeight(double towerHeight, int seconds)
{
	double ballHeight{ calculateBallHeight(towerHeight, seconds) };
	printBallHeight(ballHeight, seconds);
}

int main()
{
	double towerHeight{ getTowerHeight() };

	calculateAndPrintBallHeight(towerHeight, 0);
	calculateAndPrintBallHeight(towerHeight, 1);
	calculateAndPrintBallHeight(towerHeight, 2);
	calculateAndPrintBallHeight(towerHeight, 3);
	calculateAndPrintBallHeight(towerHeight, 4);
	calculateAndPrintBallHeight(towerHeight, 5);
       
	return 0;
}