Chapter 2  Variables and operators

This chapter describes how to write statements using variables, which store values like numbers and words, and operators, which are symbols that perform a computation. We also explain three kinds of programming errors and offer additional debugging advice.

2.1  Declaring variables

One of the most powerful features of a programming language is the ability to define and manipulate variables. A variable is a named location that stores a value. Values may be numbers, text, images, sounds, and other types of data. To store a value, you first have to declare a variable.

String message;

This statement is a declaration, because it declares that the variable named message has the type String. Each variable has a type that determines what kind of values it can store. For example, the int type can store integers, and the char type can store characters.

Some types begin with a capital letter and some with lowercase. We will learn the significance of this distinction later, but for now you should take care to get it right. There is no such type as Int or string.

To declare an integer variable named x, you simply type:

int x;

Note that x is an arbitrary name for the variable. In general, you should use names that indicate what the variables mean. For example, if you saw these declarations, you could probably guess what values would be stored:

String firstName; String lastName; int hour, minute;

This example declares two variables with type String and two with type int. When a variable name contains more than one word, like firstName, it is conventional to capitalize the first letter of each word except the first. Variable names are case-sensitive, so firstName is not the same as firstname or FirstName.

This example also demonstrates the syntax for declaring multiple variables with the same type on one line: hour and minute are both integers. Note that each declaration statement ends with a semicolon.

You can use any name you want for a variable. But there are about 50 reserved words, called keywords, that you are not allowed to use as variable names. These words include public, class, static, void, and int, which are used by the compiler to analyze the structure of the program.

You can find the complete list of keywords at, but you don’t have to memorize them. Most programming editors provide “syntax highlighting”, which makes different parts of the program appear in different colors.

2.2  Assignment

Now that we have declared variables, we want to use them to store values. We do that with an assignment statement.

message = "Hello!"; // give message the value "Hello!" hour = 11; // assign the value 11 to hour minute = 59; // set minute to 59

This example shows three assignments, and the comments illustrate different ways people sometimes talk about assignment statements. The vocabulary can be confusing here, but the idea is straightforward:

  • When you declare a variable, you create a named storage location.
  • When you make an assignment to a variable, you update its value.

As a general rule, a variable has to have the same type as the value you assign to it. For example, you cannot store a string in minute or an integer in message. We will see some examples that seem to break this rule, but we’ll get to that later.

A common source of confusion is that some strings look like integers, but they are not. For example, message can contain the string "123", which is made up of the characters '1', '2', and '3'. But that is not the same thing as the integer 123.

message = "123"; // legal message = 123; // not legal

Variables must be initialized (assigned for the first time) before they can be used. You can declare a variable and then assign a value later, as in the previous example. You can also declare and initialize on the same line:

String message = "Hello!"; int hour = 11; int minute = 59;

2.3  State diagrams

Because Java uses the = symbol for assignment, it is tempting to interpret the statement a = b as a statement of equality. It is not!

Equality is commutative, and assignment is not. For example, in mathematics if a = 7 then 7 = a. In Java a = 7; is a legal assignment statement, but 7 = a; is not. The left side of an assignment statement has to be a variable name (storage location).

Also, in mathematics, a statement of equality is true for all time. If a = b now, a is always equal to b. In Java, an assignment statement can make two variables equal, but they don’t have to stay that way.

int a = 5; int b = a; // a and b are now equal a = 3; // a and b are no longer equal

The third line changes the value of a, but it does not change the value of b, so they are no longer equal.

Taken together, the variables in a program and their current values make up the program’s state. Figure 2.1 shows the state of the program after these assignment statements run.

Figure 2.1: State diagram of the variables a and b.

Diagrams like this one that show the state of the program are called state diagrams. Each variable is represented with a box showing the name of the variable on the outside and the value inside. As the program runs, the state changes, so you should think of a state diagram as a snapshot of a particular point in time.

2.4  Printing variables

You can display the value of a variable using print or println. The following statements declare a variable named firstLine, assign it the value "Hello, again!", and display that value.

String firstLine = "Hello, again!"; System.out.println(firstLine);

When we talk about displaying a variable, we generally mean the value of the variable. To display the name of a variable, you have to put it in quotes.

System.out.print("The value of firstLine is "); System.out.println(firstLine);

For this example, the output is:

The value of firstLine is Hello, again!

Conveniently, the syntax for displaying a variable is the same regardless of its type. For example:

int hour = 11; int minute = 59; System.out.print("The current time is "); System.out.print(hour); System.out.print(":"); System.out.print(minute); System.out.println(".");

The output of this program is:

The current time is 11:59.

To output multiple values on the same line, it’s common to use several print statements followed by println at the end. But don’t forget the println! On many computers, the output from print is stored without being displayed until println is run; then the entire line is displayed at once. If you omit the println, the program might display the stored output at unexpected times or even terminate without displaying anything.

2.5  Arithmetic operators

Operators are symbols that represent simple computations. For example, the addition operator is +, subtraction is -, multiplication is *, and division is /.

The following program converts a time of day to minutes:

int hour = 11; int minute = 59; System.out.print("Number of minutes since midnight: "); System.out.println(hour * 60 + minute);

In this program, hour * 60 + minute is an expression, which represents a single value to be computed. When the program runs, each variable is replaced by its current value, and then the operators are applied. The values operators work with are called operands.

The result of the previous example is:

Number of minutes since midnight: 719

Expressions are generally a combination of numbers, variables, and operators. When complied and executed, they become a single value.

For example, the expression 1 + 1 has the value 2. In the expression hour - 1, Java replaces the variable with its value, yielding 11 - 1, which has the value 10. In the expression hour * 60 + minute, both variables get replaced, yielding 11 * 60 + 59. The multiplication happens first, yielding 660 + 59. Then the addition yields 719.

Addition, subtraction, and multiplication all do what you expect, but you might be surprised by division. For example, the following fragment tries to compute the fraction of an hour that has elapsed:

System.out.print("Fraction of the hour that has passed: "); System.out.println(minute / 60);

The output is:

Fraction of the hour that has passed: 0

This result often confuses people. The value of minute is 59, and 59 divided by 60 should be 0.98333, not 0. The problem is that Java performs “integer division” when the operands are integers. By design, integer division always rounds toward zero, even in cases like this one where the next integer is close.

As an alternative, we can calculate a percentage rather than a fraction:

System.out.print("Percent of the hour that has passed: "); System.out.println(minute * 100 / 60);

The new output is:

Percent of the hour that has passed: 98

Again the result is rounded down, but at least now it’s approximately correct.

2.6  Floating-point numbers

A more general solution is to use floating-point numbers, which can represent fractions as well as integers. In Java, the default floating-point type is called double, which is short for double-precision. You can create double variables and assign values to them using the same syntax we used for the other types:

double pi; pi = 3.14159;

Java performs “floating-point division” when one or more operands are double values. So we can solve the problem we saw in the previous section:

double minute = 59.0; System.out.print("Fraction of the hour that has passed: "); System.out.println(minute / 60.0);

The output is:

Fraction of the hour that has passed: 0.9833333333333333

Although floating-point numbers are useful, they can be a source of confusion. For example, Java distinguishes the integer value 1 from the floating-point value 1.0, even though they seem to be the same number. They belong to different data types, and strictly speaking, you are not allowed to make assignments between types.

The following is illegal because the variable on the left is an int and the value on the right is a double:

int x = 1.1; // compiler error

It is easy to forget this rule because in many cases Java automatically converts from one type to another:

double y = 1; // legal, but bad style

The preceding example should be illegal, but Java allows it by converting the int value 1 to the double value 1.0 automatically. This leniency is convenient, but it often causes problems for beginners. For example:

double y = 1 / 3; // common mistake

You might expect the variable y to get the value 0.333333, which is a legal floating-point value. But instead it gets the value 0.0. The expression on the right divides two integers, so Java does integer division, which yields the int value 0. Converted to double, the value assigned to y is 0.0.

One way to solve this problem (once you figure out the bug) is to make the right-hand side a floating-point expression. The following sets y to 0.333333, as expected:

double y = 1.0 / 3.0; // correct

As a matter of style, you should always assign floating-point values to floating-point variables. The compiler won’t make you do it, but you never know when a simple mistake will come back and haunt you.

2.7  Rounding errors

Most floating-point numbers are only approximately correct. Some numbers, like reasonably-sized integers, can be represented exactly. But repeating fractions, like 1/3, and irrational numbers, like π, cannot. To represent these numbers, computers have to round off to the nearest floating-point number.

The difference between the number we want and the floating-point number we get is called rounding error. For example, the following two statements should be equivalent:

System.out.println(0.1 * 10); System.out.println(0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1);

But on many machines, the output is:

1.0 0.9999999999999999

The problem is that 0.1, which is a terminating fraction in decimal, is a repeating fraction in binary. So its floating-point representation is only approximate. When we add up the approximations, the rounding errors accumulate.

For many applications, like computer graphics, encryption, statistical analysis, and multimedia rendering, floating-point arithmetic has benefits that outweigh the costs. But if you need absolute precision, use integers instead. For example, consider a bank account with a balance of $123.45:

double balance = 123.45; // potential rounding error

In this example, balances will become inaccurate over time as the variable is used in arithmetic operations like deposits and withdrawals. The result would be angry customers and potential lawsuits. You can avoid the problem by representing the balance as an integer:

int balance = 12345; // total number of cents

This solution works as long as the number of cents doesn’t exceed the largest integer, which is about 2 billion.

2.8  Operators for strings

In general, you cannot perform mathematical operations on strings, even if the strings look like numbers. The following expressions are illegal:

"Hello" - 1 "World" / 123 "Hello" * "World"

The + operator works with strings, but it might not do what you expect. For strings, the + operator performs concatenation, which means joining end-to-end. So "Hello, " + "World!" yields the string "Hello, World!".

Or if you have a variable called name that has type String, the expression "Hello, " + name appends the value of name to the hello string, which creates a personalized greeting.

Since addition is defined for both numbers and strings, Java performs automatic conversions you may not expect:

System.out.println(1 + 2 + "Hello"); // the output is 3Hello System.out.println("Hello" + 1 + 2); // the output is Hello12

Java executes these operations from left to right. In the first line, 1 + 2 is 3, and 3 + "Hello" is "3Hello". But in the second line, "Hello" + 1 is "Hello1", and "Hello1" + 2 is "Hello12".

When more than one operator appears in an expression, they are evaluated according to order of operations. Generally speaking, Java evaluates operators from left to right (as we saw in the previous section). But for numeric operators, Java follows mathematical conventions:

  • Multiplication and division take “precedence” over addition and subtraction, which means they happen first. So 1 + 2 * 3 yields 7, not 9, and 2 + 4 / 2 yields 4, not 3.
  • If the operators have the same precedence, they are evaluated from left to right. So in the expression minute * 100 / 60, the multiplication happens first; if the value of minute is 59, we get 5900 / 60, which yields 98. If these same operations had gone from right to left, the result would have been 59 * 1, which is incorrect.
  • Any time you want to override the order of operations (or you are not sure what it is) you can use parentheses. Expressions in parentheses are evaluated first, so (1 + 2) * 3 is 9. You can also use parentheses to make an expression easier to read, as in (minute * 100) / 60, even though it doesn’t change the result.

Don’t work too hard to remember the order of operations, especially for other operators. If it’s not obvious by looking at the expression, use parentheses to make it clear.

2.9  Composition

So far we have looked at the elements of a programming language – variables, expressions, and statements – in isolation, without talking about how to put them together.

One of the most useful features of programming languages is their ability to take small building blocks and compose them. For example, we know how to multiply numbers and we know how to display values. We can combine these operations into a single statement:

System.out.println(17 * 3);

Any arithmetic expression can be used inside a print statement. We’ve already seen one example:

System.out.println(hour * 60 + minute);

You can also put arbitrary expressions on the right side of an assignment:

int percentage; percentage = (minute * 100) / 60;

The left side of an assignment must be a variable name, not an expression. That’s because the left side indicates where the result will be stored, and expressions do not represent storage locations.

hour = minute + 1; // correct minute + 1 = hour; // compiler error

The ability to compose operations may not seem impressive now, but we will see examples later on that allow us to write complex computations neatly and concisely. But don’t get too carried away. Large, complex expressions can be hard to read and debug.

2.10  Types of errors

Three kinds of errors can occur in a program: compile-time errors, run-time errors, and logic errors. It is useful to distinguish among them in order to track them down more quickly.

Compile-time errors occur when you violate the syntax rules of the Java language. For example, parentheses and braces have to come in matching pairs. So (1 + 2) is legal, but 8) is not. In the latter case, the program cannot be compiled, and the compiler displays an error.

Error messages from the compiler usually indicate where in the program the error occurred, and sometimes they can tell you exactly what the error is. As an example, let’s get back to the hello world program from Section 1.4.

If you forget the semicolon at the end of the print statement, you might get an error message like this:

File: [line: 5] Error: ';' expected

That’s pretty good: the location of the error is correct, and the error message tells you what’s wrong.

But error messages are not always easy to understand. Sometimes the compiler reports the place in the program where the error was detected, not where it actually occurred. And sometimes the description of the problem is more confusing than helpful.

For example, if you leave out the closing brace at the end of main (line 6), you might get a message like this:

File: [line: 7] Error: reached end of file while parsing

There are two problems here. First, the error message is written from the compiler’s point of view, not yours. Parsing is the process of reading a program before translating; if the compiler gets to the end of the file while still parsing, that means something was omitted. But the compiler doesn’t know what. It also doesn’t know where. The compiler discovers the error at the end of the program (line 7), but the missing brace should be on the previous line.

Error messages contain useful information, so you should make an effort to read and understand them. But don’t take them too literally.

During the first few weeks of your programming career, you will probably spend a lot of time tracking down compile-time errors. But as you gain experience, you will make fewer mistakes and find them more quickly.

The second type of error is a run-time error, so-called because it does not appear until after the program has started running. In Java, these errors occur while the interpreter is executing byte code and something goes wrong. These errors are also called “exceptions” because they usually indicate that something exceptional (and bad) has happened.

Run-time errors are rare in the simple programs you will see in the first few chapters, so it might be a while before you encounter one. When a run-time error occurs, the interpreter displays an error message that explains what happened and where.

For example, if you accidentally divide by zero you will get a message like this:

Exception in thread "main" java.lang.ArithmeticException: / by zero at Hello.main(

Some parts of this output are useful for debugging. The first line includes the name of the exception, java.lang.ArithmeticException, and a message that indicates more specifically what happened, / by zero. The next line shows the method where the error occurred; Hello.main indicates the method main in the class Hello. It also reports the file where the method is defined,, and the line number where the error occurred, 5.

Error messages sometimes contain additional information that won’t make sense yet. So one of the challenges is to figure out where to find the useful parts without being overwhelmed by extraneous information. Also, keep in mind that the line where the program crashed may not be the line that needs to be corrected.

The third type of error is the logic error. If your program has a logic error, it will compile and run without generating error messages, but it will not do the right thing. Instead, it will do exactly what you told it to do. For example, here is a version of the hello world program with a logic error:

This program compiles and runs just fine, but the output is:

Hello, World!

Assuming that we wanted the output on one line, this is not correct. The problem is that the first line uses println, when we probably meant to use print (see the “goodbye world” example of Section 1.5).

Identifying logic errors can be hard because you have to work backwards, looking at the output of the program, trying to figure out why it is doing the wrong thing, and how to make it do the right thing. Usually the compiler and the interpreter can’t help you, since they don’t know what the right thing is.

Now that you know about the three kinds of errors, you might want to read Appendix C, where we’ve collected some of our favorite debugging advice. It refers to language features we haven’t talked about yet, so you might want to re-read it from time to time.

2.11  Vocabulary

A named storage location for values. All variables have a type, which is declared when the variable is created.
A number, string, or other data that can be stored in a variable. Every value belongs to a type (for example, int or String).
A statement that creates a new variable and specifies its type.
Mathematically speaking, a set of values. The type of a variable determines which values it can have.
The structure of a program; the arrangement of the words and symbols it contains.
A reserved word used by the compiler to analyze programs. You cannot use keywords (like public, class, and void) as variable names.
A statement that gives a value to a variable.
To assign a variable for the first time.
The variables in a program and their current values.
state diagram:
A graphical representation of the state of a program at a point in time.
A symbol that represents a computation like addition, multiplication, or string concatenation.
One of the values on which an operator operates. Most operators in Java require two operands.
A combination of variables, operators, and values that represents a single value. Expressions also have types, as determined by their operators and operands.
A data type that represents numbers with an integer part and a fractional part. In Java, the default floating-point type is double.
rounding error:
The difference between the number we want to represent and the nearest floating-point number.
To join two values, often strings, end-to-end.
order of operations:
The rules that determine in what order operations are evaluated.
The ability to combine simple expressions and statements into compound expressions and statements.
compile-time error:
An error in the source code that makes it impossible to compile. Also called a “syntax error”.
To analyze the structure of a program; what the compiler does first.
run-time error:
An error in a program that makes it impossible to run to completion. Also called an “exception”.
logic error:
An error in a program that makes it do something other than what the programmer intended.

2.12  Exercises

The code for this chapter is in the ch02 directory of ThinkJavaCode. See page ?? for instructions on how to download the repository. Before you start the exercises, we recommend that you compile and run the examples.

If you have not already read Appendix A.2, now might be a good time. It describes the DrJava Interactions Pane, which is a useful way to develop and test short fragments of code without writing a complete class definition.

Exercise 1  

If you are using this book in a class, you might enjoy this exercise. Find a partner and play “Stump the Chump”:

Start with a program that compiles and runs correctly. One player looks away while the other player adds an error to the program. Then the first player tries to find and fix the error. You get two points if you find the error without compiling the program, one point if you find it using the compiler, and your opponent gets a point if you don’t find it.

Exercise 2  

The point of this exercise is (1) to use string concatenation to display values with different types (int and String), and (2) to practice developing programs gradually by adding a few statements at a time.

  1. Create a new program named Copy or type in something like the hello world program and make sure you can compile and run it.
  2. Following the example in Section 2.4, write a program that creates variables named day, date, month, and year. The variable day will contain the day of the week (like Friday), and date will contain the day of the month (like the 13th). What type is each variable? Assign values to those variables that represent today’s date.
  3. Display (print out) the value of each variable on a line by itself. This is an intermediate step that is useful for checking that everything is working so far. Compile and run your program before moving on.
  4. Modify the program so that it displays the date in standard American format, for example: Thursday, July 16, 2015.
  5. Modify the program so it also displays the date in European format. The final output should be:
    American format: Thursday, July 16, 2015 European format: Thursday 16 July 2015
Exercise 3  

The point of this exercise is to (1) use some of the arithmetic operators, and (2) start thinking about compound entities (like time of day) that are represented with multiple values.

  1. Create a new program called From now on, we won’t remind you to start with a small, working program, but you should.
  2. Following the example program in Section 2.4, create variables named hour, minute, and second. Assign values that are roughly the current time. Use a 24-hour clock so that at 2pm the value of hour is 14.
  3. Make the program calculate and display the number of seconds since midnight.
  4. Calculate and display the number of seconds remaining in the day.
  5. Calculate and display the percentage of the day that has passed. You might run into problems when computing percentages with integers, so consider using floating-point.
  6. Change the values of hour, minute, and second to reflect the current time. Then write code to compute the elapsed time since you started working on this exercise.

Hint: You might want to use additional variables to hold values during the computation. Variables that are used in a computation but never displayed are sometimes called “intermediate” or “temporary” variables.

Text © Allen Downey and Chris Mayfield. Interactive HTML © Trinket. Both provided under a CC-NC-BY license. Book version 6.1.3.