Decimal to Multiple-Bases Conversion with Stack

Decimal to multiple-base conversion is a common programming task where we convert a decimal number to binary, octal, hexadecimal, or any other base. Using a stack data structure makes this process efficient because stacks follow the Last-In-First-Out (LIFO) principle, which naturally reverses the remainder sequence obtained during division.

How It Works

The conversion algorithm repeatedly divides the decimal number by the target base and stores remainders in a stack. When we pop elements from the stack, we get the digits in the correct order for the converted number.

Syntax

Following is the basic algorithm for decimal to any base conversion −

Stack s = new Stack();
do {
    s.Push(n % baseNum);
    n /= baseNum;
} while (n != 0);

// Pop elements to get result
while (s.Count > 0) {
    Console.Write(s.Pop());
}

Using Stack for Binary Conversion

Example

using System;
using System.Collections;

class Program {
    public static void Main() {
        int n = 45;
        int baseNum = 2; // Binary conversion
        Stack s = new Stack();
        
        Console.WriteLine("Converting " + n + " to binary:");
        
        do {
            s.Push(n % baseNum);
            n /= baseNum;
        } while (n != 0);
        
        Console.Write("Result: ");
        while (s.Count > 0) {
            Console.Write(s.Pop());
        }
        Console.WriteLine();
    }
}

The output of the above code is −

Converting 45 to binary:
Result: 101101

Using Stack for Octal Conversion

Example

using System;
using System.Collections;

class Program {
    public static void Main() {
        int n = 125;
        int baseNum = 8; // Octal conversion
        Stack s = new Stack();
        
        Console.WriteLine("Converting " + n + " to octal:");
        
        do {
            s.Push(n % baseNum);
            n /= baseNum;
        } while (n != 0);
        
        Console.Write("Result: ");
        while (s.Count > 0) {
            Console.Write(s.Pop());
        }
        Console.WriteLine();
    }
}

The output of the above code is −

Converting 125 to octal:
Result: 175

Using Stack for Hexadecimal Conversion

Example

using System;
using System.Collections;

class Program {
    public static void Main() {
        int n = 255;
        int baseNum = 16; // Hexadecimal conversion
        Stack s = new Stack();
        
        Console.WriteLine("Converting " + n + " to hexadecimal:");
        
        do {
            int remainder = n % baseNum;
            if (remainder < 10)
                s.Push(remainder);
            else
                s.Push((char)('A' + remainder - 10));
            n /= baseNum;
        } while (n != 0);
        
        Console.Write("Result: ");
        while (s.Count > 0) {
            Console.Write(s.Pop());
        }
        Console.WriteLine();
    }
}

The output of the above code is −

Converting 255 to hexadecimal:
Result: FF

Multiple Base Conversions in One Program

Example

using System;
using System.Collections;

class Program {
    public static string ConvertToBase(int number, int baseNum) {
        if (number == 0) return "0";
        
        Stack s = new Stack();
        string result = "";
        
        while (number > 0) {
            int remainder = number % baseNum;
            if (remainder < 10)
                s.Push(remainder);
            else
                s.Push((char)('A' + remainder - 10));
            number /= baseNum;
        }
        
        while (s.Count > 0) {
            result += s.Pop();
        }
        return result;
    }
    
    public static void Main() {
        int number = 156;
        
        Console.WriteLine("Number: " + number);
        Console.WriteLine("Binary (base 2): " + ConvertToBase(number, 2));
        Console.WriteLine("Octal (base 8): " + ConvertToBase(number, 8));
        Console.WriteLine("Hexadecimal (base 16): " + ConvertToBase(number, 16));
        Console.WriteLine("Base 5: " + ConvertToBase(number, 5));
    }
}

The output of the above code is −

Number: 156
Binary (base 2): 10011100
Octal (base 8): 234
Hexadecimal (base 16): 9C
Base 5: 1111

Conclusion

Using a stack for decimal to multiple-base conversion is an efficient approach because the LIFO nature of stacks naturally handles the digit ordering. This method works for any base from 2 to 36, making it a versatile solution for number system conversions.