Java Academy · Lesson

Integer Arithmetic & Overflow

Understand integer division, modulus, overflow behavior, and how to detect it.

Integer Arithmetic & Overflow is a free Java Academy lesson on CoddyKit — lesson 2 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Java Academy learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.

Integer Arithmetic & Overflow

Java integers have fixed sizes. When a calculation exceeds the maximum or minimum value, it wraps around silently — no exception is thrown. Understanding this prevents subtle bugs.

Integer Ranges

Each integer type has a bounded range determined by its bit width:

byte: -128 to 127
short: -32,768 to 32,767
int: -2,147,483,648 to 2,147,483,647
long: -9.2 × 10^18 to 9.2 × 10^18

System.out.println(Integer.MAX_VALUE); // 2147483647
System.out.println(Integer.MIN_VALUE); // -2147483648
System.out.println(Long.MAX_VALUE);    // 9223372036854775807
System.out.println(Byte.MAX_VALUE);    // 127

Overflow: Silent Wrap-Around

Adding 1 to Integer.MAX_VALUE wraps to Integer.MIN_VALUE. This is two's complement arithmetic — Java makes no guarantee and throws no exception.

int max = Integer.MAX_VALUE;
System.out.println(max + 1); // -2147483648 (overflow!)

byte b = 127;
b++;  // wraps to -128
System.out.println(b); // -128

// Real bug: counting votes in a large election with int
int votes = Integer.MAX_VALUE;
votes += 100; // silently wrong
System.out.println(votes); // negative number!

Detecting Overflow with Math.addExact

Java 8+ introduced Math.addExact(), multiplyExact(), and subtractExact() which throw ArithmeticException on overflow instead of silently wrapping.

try {
    int result = Math.addExact(Integer.MAX_VALUE, 1);
} catch (ArithmeticException e) {
    System.out.println("Overflow detected!"); // prints this
}

try {
    long safe = Math.multiplyExact(100_000L, 100_000L);
    System.out.println(safe); // 10000000000
} catch (ArithmeticException e) {
    System.out.println("Multiply overflow");
}

Integer Division and Modulus

Integer division truncates toward zero. The % operator gives the remainder with the sign of the dividend. Watch out for division by zero — it throws ArithmeticException.

System.out.println(10 / 3);    // 3 (not 3.33)
System.out.println(10 % 3);    // 1
System.out.println(-10 % 3);   // -1 (sign follows dividend)
System.out.println(-10 % -3);  // -1

try {
    int x = 5 / 0; // ArithmeticException: / by zero
} catch (ArithmeticException e) {
    System.out.println(e.getMessage()); // / by zero
}

// Float division by zero gives Infinity, not exception
System.out.println(5.0 / 0); // Infinity

Long Arithmetic for Large Numbers

Use long when values may exceed int range. Always append L to long literals to prevent overflow before the assignment.

// Bug: multiplication done as int, then widened
long wrong = 1_000_000 * 1_000_000;   // overflows int!
System.out.println(wrong); // -727379968 (wrong!)

// Fix: one operand is long
long correct = 1_000_000L * 1_000_000L;
System.out.println(correct); // 1000000000000

// Or cast first
long alsOk = (long) 1_000_000 * 1_000_000;
System.out.println(alsOk); // 1000000000000

Bit Shift Operators

Bit shift operators are fast ways to multiply/divide by powers of 2:

n << k — left shift: multiply by 2^k
n >> k — signed right shift: divide by 2^k
n >>> k — unsigned right shift: fills with 0s

int n = 8;
System.out.println(n << 1);  // 16 (8 * 2)
System.out.println(n << 2);  // 32 (8 * 4)
System.out.println(n >> 1);  // 4  (8 / 2)
System.out.println(n >> 2);  // 2  (8 / 4)

// Check if number is power of 2
boolean isPow2 = n > 0 && (n & (n - 1)) == 0;
System.out.println(isPow2); // true

Bitwise AND, OR, XOR

Bitwise operators work on individual bits and are used in permissions, flags, and low-level protocols.

int a = 0b1010; // 10
int b = 0b1100; // 12

System.out.println(Integer.toBinaryString(a & b)); // 1000 (AND = 8)
System.out.println(Integer.toBinaryString(a | b)); // 1110 (OR  = 14)
System.out.println(Integer.toBinaryString(a ^ b)); // 0110 (XOR = 6)
System.out.println(Integer.toBinaryString(~a));    // ...11110101 (NOT)

// Permission flags example
int READ  = 0b001;
int WRITE = 0b010;
int EXEC  = 0b100;
int perms = READ | WRITE; // user has read+write
System.out.println((perms & EXEC) != 0); // false — no exec

Underscores in Numeric Literals

Java 7+ allows underscores in numeric literals to improve readability. They are ignored by the compiler.

int million = 1_000_000;
long creditCard = 4_111_1111_1111_1111L;
double pi = 3.141_592_653_589_793;
int hex = 0xFF_EC_D1_2E;
int binary = 0b0001_0101_0110;

System.out.println(million);   // 1000000
System.out.println(creditCard); // 4111111111111111

BigInteger for Arbitrary Precision

When values exceed long, use BigInteger. It has no overflow but is slower than primitives. Use it for cryptographic keys, factorials, and astronomical numbers.

import java.math.BigInteger;

BigInteger factorial100 = BigInteger.ONE;
for (int i = 2; i <= 100; i++) {
    factorial100 = factorial100.multiply(BigInteger.valueOf(i));
}
System.out.println(factorial100.toString().length() + " digits"); // 158 digits

BigInteger a = new BigInteger("999999999999999999999999999999");
BigInteger b = new BigInteger("1");
System.out.println(a.add(b)); // 1000000000000000000000000000000

Practical: Overflow-Safe Counter

A pattern for implementing a counter that handles overflow safely by using Math.addExact and falling back to Long.MAX_VALUE.

class SafeCounter {
    private long count = 0;

    public void increment() {
        try {
            count = Math.addExact(count, 1L);
        } catch (ArithmeticException e) {
            count = Long.MAX_VALUE; // cap at max
        }
    }

    public long get() { return count; }
}

SafeCounter sc = new SafeCounter();
sc.increment();
sc.increment();
System.out.println(sc.get()); // 2

Quick Check

What is the value of the following expression?

long result = 1_000_000 * 1_000_000;
System.out.println(result);

Recap: Integer Arithmetic & Overflow

Key takeaways:

Integer overflow wraps around silently — no exception by default
Use Math.addExact/multiplyExact/subtractExact to catch overflow
Integer division truncates toward zero; % sign follows dividend
Use long literals (L suffix) when intermediate results may overflow int
BigInteger handles arbitrarily large values without overflow
Bit shift operators are fast alternatives to power-of-2 multiply/divide

Frequently asked questions

Is the “Integer Arithmetic & Overflow” lesson free?

Yes — the full text of “Integer Arithmetic & Overflow” is free to read here on the web, and the Java Academy course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Java Academy course, upgrade to CoddyKit PRO.

What will I learn in “Integer Arithmetic & Overflow”?

Understand integer division, modulus, overflow behavior, and how to detect it. You practise Java Academy with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.

Do I need any experience to start Java Academy?

No prior experience is required. Java Academy on CoddyKit is structured for beginners through advanced learners; this is — lesson 2 of 4, so you can start here or from the beginning and move at your own pace.

How long does the “Integer Arithmetic & Overflow” lesson take?

Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.

Can I write and run code in this Java Academy lesson?

Yes. Every Java Academy lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.

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