IEEE 754 Floating Point Representation & BigDecimal

1Concept

Binary floating point types (float and double) follow the IEEE 754 binary floating-point standard. Because decimal numbers like 0.1 cannot be represented precisely in binary base-2, calculations like 0.1 + 0.2 yield 0.30000000000000004. Financial and accounting software must use java.math.BigDecimal with String constructors.

2Architecture Diagram

Double Binary Storage:  0.1 + 0.2  ---> 0.30000000000000004 (Imprecise!)
BigDecimal Storage:     new BigDecimal("0.1").add(new BigDecimal("0.2")) ---> 0.3 (Exact Precision!)

3Code Example

import java.math.BigDecimal;
import java.math.RoundingMode;

public class PreciseMonetaryDemo {
    public static void main(String[] args) {
        double d1 = 0.1;
        double d2 = 0.2;
        System.out.println("double 0.1 + 0.2: " + (d1 + d2));

        BigDecimal b1 = new BigDecimal("0.1");
        BigDecimal b2 = new BigDecimal("0.2");
        BigDecimal sum = b1.add(b2);
        System.out.println("BigDecimal '0.1' + '0.2': " + sum);

        BigDecimal num = new BigDecimal("10");
        BigDecimal den = new BigDecimal("3");
        BigDecimal result = num.divide(den, 4, RoundingMode.HALF_UP);
        System.out.println("10 / 3 (4 decimals): " + result);
    }
}

4Expected Output

double 0.1 + 0.2: 0.30000000000000004
BigDecimal '0.1' + '0.2': 0.3
10 / 3 (4 decimals): 3.3333

5Key Takeaways

• ✓NEVER use double or float for currency or financial calculations.
• ✓ALWAYS construct BigDecimal using String constructors: new BigDecimal("0.1"), NOT new BigDecimal(0.1).
• ✓Division with BigDecimal requires explicit RoundingMode to prevent ArithmeticException on non-terminating decimals.