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Java Integer Arithmetic For Beginners

written by: Noel Kalicharan•edited by: J. F. Amprimoz•updated: 12/26/2008

In this article, we discuss some basic ideas of integer arithmetic in Java. In particular, we show how integer expressions are formed using “arithmetic operators". We also explain how expressions are evaluated based on “operator precedence".

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    Integer arithmetic expressions in Java

    In Java, integer arithmetic is performed using "integer data types". In Java Data Types, we discussed some of these types—byte, short, int and long—and gave examples of "integer constants". An integer constant (e.g. 23, 0, -245) is the simplest example of an integer expression. However, most of the time, we write integer expressions by combining constants and variables with the following arithmetic operators:

    Java Integer Arithmetic 

    For example, suppose we have the following declaration:

    int a, b, c;

    then the following are all valid expressions:

    a + 39

    a + b - c * 2

    b % 10 //the remainder when b is divided by 10

    c + (a * 2 + b * 2) / 2

    The operators +, - and * all give the expected results. However, / performs integer division; if there is any remainder, it is thrown away. We say integer division truncates. Thus 19 / 5 gives the value 3; the remainder 4 is discarded.

    But what is the value of -19 / 5? The answer here is –3. The rule is that, in Java, integer division truncates towards zero. Since the exact value of –19 ÷ 5 is –3.8, truncating towards zero gives –3.

    The % operator gives the remainder when one integer is divided by another; for example,

    19 % 5 evaluates to 4;

    j % 7 gives the remainder when j is divided by 7;

    You can use it to test, for instance, if a number j is even or odd. If j % 2 is 0 then j is even; if j % 2 is 1, j is odd.

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    Precedence of operators

    Java evaluates an arithmetic expression based on the usual precedence of operators: multiplication and division are done before addition and subtraction. We say that multiplication and division have higher precedence than addition and subtraction. For example, the expression

    5 + 3 * 4

    is evaluated by first multiplying 3 by 4 (giving 12) and then adding 5 to 12, giving 17 as the value of the expression.

    As usual, we can use brackets to force the evaluation of an expression in the order we want. For example,

    (5 + 3) * 4

    first adds 5 and 3 (giving 8), and then multiplies 8 by 4, giving 32.

    When two operators which have the same precedence appear in an expression, they are evaluated from left to right, unless specified otherwise by brackets. For example,

    24 / 4 * 2

    is evaluated as

    (24 / 4) * 2

    (giving 12) and

    12 - 7 + 3

    is evaluated as

    (12 - 7) + 3

    giving 8. However,

    24 / (4 * 2)

    is evaluated with the multiplication done first, giving 3, and

    12 - (7 + 3)

    is evaluated with the addition done first, giving 2.

    In Java, the remainder operator % has the same precedence as multiplication (*) and division (/).

    In Floating Point Numbers and Expressions, we explain how to work with floating-point numbers. In Java double to int and Other Conversions, we show how to mix integers and floating-point numbers in the same expression.

    Exercise: What is printed by the following program? Check your answer by typing the program to a file Exercise.java. Compile the program and run it.

    public class Exercise {

    public static void main(String[] args) {

    int a = 15;

    int b = 24;

    System.out.printf("%d %d\n", b - a + 7, b - (a + 7));

    System.out.printf("%d %d\n", b - a - 4, b - (a - 4));

    System.out.printf("%d %d\n", b % a / 2, b % (a / 2));

    System.out.printf("%d %d\n", b * a / 2, b * (a / 2));

    System.out.printf("%d %d\n", b / 2 * a, b / (2 * a));

    }

    }

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    References

    Java Programming – A Beginner’s Course

    Related programming references

    Article: Java Programming Tutorials: Java Integer Arithmetic