Programming Session Day 8: Manual Octal and Decimal Conversion in Java

Day 8: Manual Octal ↔ Decimal Conversion with Integers Only

1. Octal → Decimal (Input as int)

public static int octalToDecimal(int octal) {
    int decimal = 0;
    int place   = 1;         // 8^0 initially

    while (octal > 0) {
        int digit = octal % 10;      // rightmost digit (0–7)
        decimal += digit * place;    // add digit * current power of 8
        place *= 8;                  // next power of 8
        octal /= 10;                 // shift right one digit
    }

    return decimal;
}

// Example:
System.out.println(octalToDecimal(17));   // prints 15

How it works

• % 10 extracts the least-significant digit of the octal number.
• place tracks powers of 8 (1, 8, 64, ...).
• Multiply digit by place, add to total, then update both place and octal.

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2. Decimal → Octal (Output as int)

public static int decimalToOctal(int decimal) {
    int octal  = 0;
    int factor = 1;         // 10^0 for placing digits in decimal slots

    while (decimal > 0) {
        int remainder = decimal % 8;   // next octal digit
        octal += remainder * factor;   // place digit at correct decimal position
        decimal /= 8;                  // move to next digit in base 8
        factor *= 10;                  // shift factor to next decimal place (10, 100, ...)
    }

    return octal;
}

// Example:
System.out.println(decimalToOctal(15));  // prints 17

How it works

• % 8 gets the least-significant octal digit.
• Each digit is placed in the decimal representation by multiplying by factor (1, 10, 100, ...).
• Update decimal, and increase factor for the next digit.

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3. Complete Utility Class

public class ManualBaseConverter {

    public static int octalToDecimal(int octal) {
        int decimal = 0;
        int place   = 1;
        while (octal > 0) {
            int digit = octal % 10;
            decimal += digit * place;
            place *= 8;
            octal /= 10;
        }
        return decimal;
    }

    public static int decimalToOctal(int decimal) {
        int octal  = 0;
        int factor = 1;
        while (decimal > 0) {
            int remainder = decimal % 8;
            octal += remainder * factor;
            decimal /= 8;
            factor *= 10;
        }
        return octal;
    }

    public static void main(String[] args) {
        System.out.println("Octal 17 → Decimal " + octalToDecimal(17));
        System.out.println("Decimal 15 → Octal " + decimalToOctal(15));
    }
}

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Day 8 Key Takeaways

• Pure integer arithmetic: no string operations or library calls.
• Octal → Decimal: extract digits with %10, accumulate using an ever‑increasing place multiplier of 8.
• Decimal → Octal: extract base‑8 digits with %8, build the octal number in decimal slots via an increasing factor multiplier of 10.