using System;

namespace myApp

{

    public class Program

    {

        public static void Main(string[] args)

        {

            Console.WriteLine($"Adding 1001 + 1010 = {BinaryAdd("1001", "1010")}");

        }

​

        private static string BinaryAdd(string num1, string num2)

        {

            var reversed1 = Reverse(num1);

            var reversed2 = Reverse(num2);

            var carry = 0;

            var output = new System.Text.StringBuilder();

            for (var i = 0; i < (reversed1.Length > reversed2.Length ? reversed1.Length : reversed2.Length); i++)

            {

                var digit1 = reversed1[i];

                var digit2 = reversed2[i];

                if (carry > 0)

                {

                    carry--;

                    if (digit1 == '0' && digit2 == '0')

                        output.Append(1);

                    else if ((digit1 == '0' && digit2 == '1') || (digit1 == '1' && digit2 == '0'))

                    {

                        output.Append(0);

                        carry++;

                    }

                    else if (digit1 == '1' && digit2 == '1')

                    {

                        output.Append(1);

                        carry++;

                    }

                }

                else

                {

                    if (digit1 == '0' && digit2 == '0')

                        output.Append(0);

                    else if ((digit1 == '0' && digit2 == '1') || (digit1 == '1' && digit2 == '0'))

                        output.Append(1);

                    else if (digit1 == '1' && digit2 == '1')

                    {

                        output.Append(0);

                        carry++;

                    }

                }

            }

            if (carry > 0)

                for (; carry > 0; carry--)

                    output.Append(1);

            return Reverse(output.ToString());

        }

​

        private static string Reverse(string @in)

        {

            var reverseSb = new System.Text.StringBuilder();

            foreach (var digit in @in)

                reverseSb.Insert(0, digit);

            var reverse = reverseSb.ToString();

            return reverse;

        }

    }

}