Introduction

int a = 5, b = 2;
System.out.println(a / b);
System.out.println((double)a / b);
System.out.println((int)3.9);
System.out.println((int)(3.9 + 0.5));

2
2.5
3
4

Casting in Java

public class CastDemo {
    public static void main(String[] args) {
        int a = 7, b = 2;
        System.out.println(a / b);          // 3  (int division)
        System.out.println((double)a / b);  // 3.5 (promoted to double before divide)

        double d = 5.9;
        int t = (int) d;                    // 5  (truncate toward 0)
        System.out.println(t);

        // Rounding to nearest int (per CED):
        int rPos = (int)(d + 0.5);          // 6  (non-negative rounding)
        double n = -5.9;
        int rNeg = (int)(n - 0.5);          // -6 (negative rounding)
        System.out.println(rPos + " " + rNeg);
    }
}
CastDemo.main(null);

3
3.5
5
6 -6

Range and Overflow in Java Integers

int max = Integer.MAX_VALUE;  //  2147483647
int min = Integer.MIN_VALUE;  // -2147483648

System.out.println(max + 1);  // overflow → -2147483648
System.out.println(min - 1);  // overflow →  2147483647

-2147483648
2147483647

Python Helper


# Utilities to simulate Java 32-bit signed int in Python
INT_MIN = -2**31
INT_MAX =  2**31 - 1
MASK32  =  0xFFFFFFFF

def to_int32(x: int) -> int:
    x &= MASK32
    # convert to signed
    return x if x <= INT_MAX else x - (1 << 32)

def add_int32(a: int, b: int) -> int:
    return to_int32(a + b)

def sub_int32(a: int, b: int) -> int:
    return to_int32(a - b)

def mul_int32(a: int, b: int) -> int:
    return to_int32(a * b)

def div_int32(a: int, b: int) -> int:
    # Java int division truncates toward zero
    if b == 0:
        raise ZeroDivisionError("division by zero")
    q = int(a / b)  # Python truncates toward zero for int()
    return to_int32(q)

def mod_int32(a: int, b: int) -> int:
    # Java remainder has same sign as dividend (a)
    if b == 0:
        raise ZeroDivisionError("mod by zero")
    q = div_int32(a, b)
    r = to_int32(a - q * b)
    return r

# Demo
print("INT_MIN, INT_MAX:", INT_MIN, INT_MAX)
print("Overflow examples:")
print("MAX+1 =", add_int32(INT_MAX, 1))
print("MIN-1 =", sub_int32(INT_MIN, 1))
print("(-7)/2  =", div_int32(-7, 2), "  (-7)%2 =", mod_int32(-7, 2))
print("(7)/-2  =", div_int32(7, -2), "  (7)%-2 =", mod_int32(7, -2))


INT_MIN, INT_MAX: -2147483648 2147483647
Overflow examples:
MAX+1 = -2147483648
MIN-1 = 2147483647
(-7)/2  = -3   (-7)%2 = -1
(7)/-2  = -3   (7)%-2 = 1

Truncation vs. Rounding


def java_truncate(x: float) -> int:
    # Casting double->int truncates toward 0
    return int(x)  # Python int() also truncates toward 0

def ced_round(x: float) -> int:
    if x >= 0:
        return int(x + 0.5)
    else:
        return int(x - 0.5)

tests = [5.1, 5.5, 5.9, -5.1, -5.5, -5.9, 0.49, -0.49]
for v in tests:
    print(f"x={v:5}  truncate={java_truncate(v):3}  ced_round={ced_round(v):3}")


x=  5.1  truncate=  5  ced_round=  5
x=  5.5  truncate=  5  ced_round=  6
x=  5.9  truncate=  5  ced_round=  6
x= -5.1  truncate= -5  ced_round= -5
x= -5.5  truncate= -5  ced_round= -6
x= -5.9  truncate= -5  ced_round= -6
x= 0.49  truncate=  0  ced_round=  0
x=-0.49  truncate=  0  ced_round=  0

Promotion Rules

int a = 3, b = 2;
double x = a / b;          // 1.0   (int division then widened)
double y = (double)a / b;  // 1.5   (promoted before divide)

System.out.println("x = " + x);
System.out.println("y = " + y);

x = 1.0
y = 1.5

Practice: predict the output (Java)

Q1

My answers: 2, 2, 2.0, 2.5

int a = 10, b = 4;
System.out.println(a / b);
System.out.println(a % b);
System.out.println((double)(a / b));
System.out.println((double)a / b);

2
2
2.0
2.5

Q2

My Answers: -2, -3, 3

double d = -2.6;
System.out.println((int)d);
System.out.println((int)(d - 0.5));
System.out.println((int)(-d + 0.5));

-2
-3
3

Q3

My Answers: 2147483647, -2147483647

int x = Integer.MAX_VALUE;
int y = x + 2;
System.out.println(x);
System.out.println(y);

2147483647
-2147483647

FRQ-style tasks

FRQ 1. Average with correct casting Write a method avgInt that takes two int values and returns their average as a double, preserving the .5 if present.

public static double avgInt(int a, int b) {
    return (a + b) / 2.0;
}

FRQ 2. Percentage Given int correct and int total, compute the percentage as a double from 0.0 to 100.0 without losing fractional precision.

public static double gradePoint(int earnedPoints, int maxPoints) {
    if (maxPoints == 0) return 0.0;
    return 4.0 * earnedPoints / (double) maxPoints;
}

FRQ 3. Safe remainder Implement safeMod(int a, int b) that returns a % b, but if b == 0, it should return 0 instead of throwing.

public static int safeDivide(int numerator, int denominator) {
    if (denominator == 0) return 0;
    return numerator / denominator;
}

MCQs

double x = 7.9;
int y = (int) x;
System.out.println(y);

7

int a = 10;
double b = 5.5;

int c = (int)(a + b);
int c = a + (int)b;


int num = 9 / 2;
System.out.println(num);

4

double d = 15.7;
int i = (int)(d + 0.5);
System.out.println(i);

16