Question

Write methods that accomplish each of the following tasks: a) Calculate the integer part of the quotient when integer a is divided by integer b. b) Calculate the integer remainder when integer a is divided by integer b. c) Use the methods developed in parts (a) and (b) to write a method displayDigits that receives an integer between 1 and 99999 and displays it as a sequence of digits, separating each pair of digits by two spaces. For example, the integer 4562 should appear as 4562 Incorporate the methods into an application that inputs an integer and calls displayDigits by passing the method the integer entered. Display the results.

Short answer

Implement two methods, quotient and remainder, for integer division and modulo operations. Then, develop the displayDigits method to decompose an integer and display its digits with spaces between them. Finally, integrate these methods into an application that takes user input and displays the digits accordingly.

Step-by-step solution

Create Method for Integer Quotient

Define a method, named quotient, which takes two integer parameters, a and b. This method should use integer division to calculate the floor division of a by b, i.e., the integer part of the quotient when a is divided by b. The return type of this method should be an integer.

Create Method for Integer Remainder

Define another method, named remainder, which also takes two integer parameters, a and b. This method should return the remainder of the division of a by b using the modulo operator. The return type should be an integer.

Create displayDigits Method

Define a method called displayDigits that takes a single integer parameter. This method should decompose the number into individual digits and print them separated by two spaces. Use a loop to divide the number by 10 repeatedly, collecting the remainders, until the number is 0, and then print the digits in reverse order.

Incorporating Methods into the Application

Within the main part of your application, prompt the user to input an integer. Call displayDigits with this integer and display the result, as specified. Make sure to use the quotient and remainder methods created in steps 1 and 2 to build the displayDigits method.

Testing and Validation

After implementing the methods, test the application with various inputs, including edge cases like the smallest and largest numbers in the specified range (1 and 99999), to ensure accuracy and correct error handling.

Key concepts

Quotient Calculation

The quotient calculation is a basic arithmetic operation where one number, called the dividend, is divided by another, called the divisor, to find how many whole times the divisor fits into the dividend. In Java, this operation is carried out using the division (\(/\)) operator.

When dealing with integers, Java performs integer division, which can be thought of as division without the remainder or the fractional part. For example, dividing 7 by 3 would give us a quotient of 2, since 3 fits into 7 twice, wholly. The calculation would look something like this: \( \text{quotient} = \text{integer a} / \text{integer b} \).

The importance of the quotient calculation in programming cannot be overstated. It is essential for tasks like distributing items evenly, calculating page numbers, and in our case, breaking down numbers into separate digits. Essential to note is that any fractional part is discarded in integer division, ensuring that the result is always an integer.

Remainder Operation

While the quotient tells us how many times a number fits into another, the remainder operation tells us what is left over after this division. In Java, the remainder is found using the modulo (\(%\)) operator. This operator gives the residue of the division that quotient calculation doesn't account for. If we continue with our previous example where 7 is divided by 3, the remainder is 1 because 3 times 2 is 6, and there’s a leftover of 1 to reach 7.

The syntax for finding a remainder in Java is similar to the division operation: \( \text{remainder} = \text{integer a} % \text{integer b} \).

The remainder operation is crucial for various algorithms involving divisibility, like checking for even or odd numbers, implementing cyclic buffers, or as we see in our textbook example, aiding in the process of separating digits of a larger number.

Digit Separation

Digit separation is the process of breaking a number into its individual digits. This is particularly useful for formatting numbers, creating digital animations, and in mathematical computations that involve digit-by-digit analysis. In our textbook exercise, we use the aforementioned quotient and remainder Java methods to accomplish this task.

The approach uses a loop to repeatedly apply the remainder operation by dividing the number by 10 and collecting each remainder. Each remainder represents a digit from the original number. After collecting a digit, we use the quotient operation to divide the number by 10, effectively 'shifting' all digits to the right by one place, in preparation for capturing the next digit. This process continues until the original number is reduced to 0.

Executing this digit separation correctly is paramount for the clear presentation of numbers, as required in our exercise, which asks us to display each digit separated by two spaces.

Java Methods

Java methods are reusable blocks of code that perform a specific task and can be called upon when needed. They help in organizing code, reducing redundancy, and enhancing readability. In the context of our textbook solution, we define separate methods for each specific task: calculating the quotient and remainder, and separating digits.

Each method is defined with particular input parameters it operates on, ensuring encapsulation and modularity. In this way, methods like `quotient` and `remainder` can be easily utilized in various parts of a program, or in different programs altogether, without rewriting the same piece of code.

Properly defining and using methods is key to efficient programming. Through the exercise provided, students learn to craft specific functions for tasks and utilize them to build more complex operations, such as a method `displayDigits` which employs both quotient and remainder methods to achieve its goal.