Simple Arithmetic in Java Simple Arithmetic in Java You have already seen how to use Java to read and write strings of text. As we all know, computers are wonderful at dealing with numbers. This set of exercises will introduce you to simple arithmetic calculations in Java, as well as some new types of variables used to store numbers. Solutions are available here. Copies of the code in these notes can be found in the directory:
/import/teaching/BSc/1st/ItP
Adding two numbers Consider the program below, which adds two numbers together and prints the result on the screen. The program can be found in the file /import/teaching/BSc/1st/ItP/Prog21.java.
1 class Prog21 {
2 // A program to add two numbers together
3
4 public static void main(String[] args) {
5 int i = 10;
6 int j = 20;
7 i = i + j;
8 System.out.println("The sum is: " + i);
9 }
10 }
Lines 5 and 6 are variable declarations with initialisers, similar to those you have already seen in the HelloYou programs. However, in this program we want our variables to hold numbers rather than text strings, so we declare i and j as type int instead of String. The word 'int' is Java shorthand for 'integer', that is, a number with no fractional part. 27, -16 and 0 are all examples of integers, whereas 42.7 is not. An important point to note is that the integer '10' is not necessarily stored by the computer as the two digits '1' and '0'. Numbers will usually be stored in a respresentation that is easier (and faster) for the computer to understand, but not particularly readable for humans. We will return to this subject later in the exercise set when we cover reading numbers from the keyboard. Line 7 adds together the numbers stored in i and j and stores the sum back into i. Note that the previous value of i is destroyed by this operation. Variables can be treated as named 'storage boxes' in the memory of the computer, where each box can hold a single item of a particular type (text string, integer, etc). Assigning a new value to the box named i means that the old contents of the box must be thrown away. Line 8 should be familiar to you already. It prints out the text The sum is: followed by the number stored in i. As before, the plus symbol is used to join together the two strings to be printed. But i is an integer, not a string! How does this work? The Java compiler knows that println requires a string to print, so it arranges to convert the value of i into its string representation when the command is executed. This automatic conversion feature will work for most Java types, converting them to text strings that can be printed out or otherwise displayed. Most other programming languages offer similar features for easily displaying values of different types. Unfortunately, automatic conversions in the other direction, from a text string to a number, are not generally provided. As well as addition, several other basic arithmetic operations are provided by Java. These include subtraction, multiplication, division and remainder, represented by the symbols '-', '*', '/' and '%' respectively. Experiment with changing the program to use these different operations. Do you always get the results you expect, particularly when using the division and remainder operations? Exercises What is the value in i after executing the following program segments?
int i = 12;
int j = 5;
i = i / j;
int i = 12;
int j = 5;
i = i % j;
int i = 10;
int j = 5;
i = i / j;
The answers to exercises 1.1 and 1.3 are the same. Explain why. More complex arithmetic More complicated arithmetic expressions cn be written quite easily. The program below shows one example of combining the various operators in a more interesting calculation (this program can be found in the file Prog22.java in the usual directory).
1 class Prog22 {
2 // A more interesting calculation
3
4 public static void main(String[] args) {
5 int i = 12;
6 int j = 20;
7 int k = 5;
8 i = i * 6 + j / 2 - k;
9 System.out.println("The answer is: " + i);
10 }
11 }
You should experiment with some different calculations of your own and see if you always obtain the results you expect: especially when combining multiplication and division with addition and subtraction. For example, the program above produces an answer of 77, whereas you might expect the result to be 41: (12 times 6 = 72; 72 plus 20 = 92; 92 divided by 2 = 46; 46 minus 5 = 41). What's going on here? It turns out that Java's arithmetic operations have a built in 'priority', so that multiplications, divisions and remainders are evaluated before additions and subtractions. In Prog22, Java will first calculate 12 times 6 = 72; then 20 divided by 2 = 10; then 72 + 10 = 82; and finally 82 minus 5 = 77. You can use parentheses '(' and ')' to force a particular order of evaluation: anything inside parentheses is calculated before the rest of the expression. So to evaluate the expression in Prog22 in strict left-to-right order you would use:
i = (i * 6 + i) / 2 - k;
which should produce the desired answer of 41. As a matter of style and readability it is often desirable to include parentheses in expressions even when the default operator priority does exactly what you want. If we write the original calculation from Prog22 as:
i = (i * 6) + (i / 2) - k;
the parentheses do not change the result, but make the program much easier for a human being to read and understand. Exercises What is the value of i after executing the following code segments? Assume that the variables have been initialised to i = 21, j = 42 and k = 11;
i = 4 * (j + 16) % k;
i = i - j + k * 7;
i = (i - j + k) * 7;
Explain why the answers to exercises 3.2 and 3.3 are different. More on integer variables Although we have said that a Java int variable holds an 'integer' value, the two are in fact not exactly the same thing. The mathematical definitionof integers includes all positive and negative numbers with no fractional part; clearly, there must be an infinite number of different integers. However, because of the way the Java compiler is written (and the way that most computers internally represent numbers) each Java int variable must fit within a small, fixed amount of memory. This means that an int can only represent a subset of the true integers. To illustrate this point, compile and run the program below:
1 class Prog23 {
2 // A program to demonstrate integer overflow
3
4 public static void main(String[] args) {
5 int i = 2000000000;
6 int j = 2000000000;
7 i = i + j;
8 System.out.println("i + j = " + i);
9 }
10 }
The correct answer is, of course, 4000000000. Unfortunately this number is too large to fit in an int variable, so the program prints an incorrect result. When this occurs, we say that the answer has overflowed the range of the variable. Note that the exact incorrect answer printed is not important at this stage, the program simply serves as an example of the overflow effect. Exercises Modify Prog23 so that it will print both the largest (most positive) and smallest (most negative) values that will fit into a Java int variable. The Java language supports two other types of 'integer' variables: long and short. Produce two further modified versions of Prog23 that print the largest and smallest possible values of a long and a short respectively. Note: long variables should be initialised using commands such as:
long l;
l = 2042L;
or
long l = 2042L;
Where the 'L' character indicates that the value should be treated as a long instead of a normal int. No special syntax is necessary when initialising variables of type short. Reading numbers from the keyboard You have already seen how to print numeric values on the screen; Java provides a useful automatic conversion of numbers into text strings for display purposes. The reverse conversion is not provided -- there is no automatic facility in the Java language itself for converting strings to integers (or any other non-string type). Fortunately the large collection of supporting classes supplied with Java comes to the rescue. In this example we will make use of the Integer class which contains a set of methods for transforming integers to and from strings and other numeric types. The program below shows how to read a single integer from the keyboard and display it on the screen:
1 import java.io.*;
2
3 class Prog24 {
4 // Read an integer value from the keyboard
5
6 public static void main(String[] args) throws NumberFormatException, IOException {
7 int i;
8 String num;
9 BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
10
11 System.out.print("Please enter an integer: ");
12 num = in.readLine();
13 i = Integer.parseInt(num);
14 System.out.println("You typed: " + i);
15 }
16 }
Most of this program, down as far as line 12, should be quite familiar to you. Line 12 reads a line of input from the keyboard as a string text: at this point the program neither knows nor cares whether the text might represent a number, someone's name or anything else. Line 13 uses the parseInt method from the Integer class to attempt to extract an integer value from the text that was entered. The term parse refers to the process of assigning structure to an unstructured collection of text or other raw data. Parsing is the first step carried out by most compilers, taking the raw text of the program and breaking it down into classes, methods, declarations, method calls, etc. In this case, the parsing task consists of determining whether the entered text could represent an integer value and if so, assigning that value to i. If the text does not respresent a valid integer (for instance, if you were to enter '19.8' or 'foo42', the parseInt method will throw a NumberFormatException. You should try entering some invalid text to see what happens when the exception is thrown. A method such as parseInt would be relatively difficult and complex to write from scratch, as it has to carry out a large amount of so-called error checking to make sure that the text it is given does in fact represent an integer. You will find as you start to write larger programs, especially when these process input that you have no control over, that a significant amount of code is concerned with just checking for, and dealing with, all of the things that could possibly go wrong. Most of the time -- when there is nothing wrong with the input -- this code does nothing, but it is important for it to be there when some bad input does come along. Having the program simply terminate after producing an obscure error message, as Prog24 does when given bad input, is usually not an acceptable solution. In future weeks you will learn how to 'catch' exceptions and other error conditions thrown by your programs and respond to them in an appropriate way. Exercises Modify Prog24 so that it reads two integers from the keyboard, then prints their sum, difference, product, quotient and remainder after division. Modify your program further to use longs instead of ints. (Hint: Look at the methods provided by the Long class. Written by Scott Mitchell. Updated by Matthew Huntbach These notes were produced as part of the course Introduction to Programming as it was given in the Department of Computer Science at Queen Mary, University of London during the academic years 1998-2001. Last modified: 30 Sep 1999
