using System;

using System.Text;

public class Program

{

    public static void Main()

    {

        string s1 = "101";

        string s2 = "10010";

        Console.WriteLine("Sum of {0} and {1} is: {2}", s1, s2, BinaryStringSum(s1, s2));

    }

    public static string BinaryStringSum(string s1, string s2) 

    {

        var s1LastIndex = s1.Length - 1;

        var s2LastIndex = s2.Length - 1;

        StringBuilder sum = new StringBuilder();

        char carryOver = '0';

        while (s1LastIndex > 0 || s2LastIndex > 0)

        {

            Console.WriteLine(s1[s1LastIndex]);

            Console.WriteLine(s2[s2LastIndex]);

            var x = AddStringBits(s1[s1LastIndex], s2[s2LastIndex], carryOver);

            sum.Insert(0, x.sum);

            carryOver = x.carry;

            s1LastIndex--;

            s2LastIndex--;

        }

        return sum.ToString();

    }

    public static BinaryString AddStringBits(char s1, char s2, char carryOver)

    {   

        if (s1 == '1' && s2 == '1')

        {

            if (carryOver == '1')

            {

                return new BinaryString {

                    sum = '1',

                    carry = '1'

                };

            }

            else

            {

                return new BinaryString {

                    sum = '0',

                    carry = '1'

                };

            }

        }

        if ((s1 == '1' && s2 == '0') || (s1 == '0' && s2 == '1'))

        {

            if (carryOver == '1')

            {

                return new BinaryString {

                    sum = '0',

                    carry = '1'

                };

            }

            else 

            {

                return new BinaryString {

                    sum = '1',

                    carry = '0'

                };

            }

        }

        return new BinaryString {

            sum = '0',

            carry = carryOver

        };

    }

}

​

​

public class BinaryString

{

    public char sum;

    public char carry;

}