Multiple without multication or addition operator

Given two binary strings, return their sum (also a binary string).
For example,
a = "1101" // 13
b = "1000" // 8
Return “1101000”. // 104
Solution: implement Binary add to perform multication

static int MultipleWithoutOperator(int num, int multiplier)
{
    StringBuilder sb = new StringBuilder();
    string binary = Convert.ToString(num, 2);
    string binaryMultiplier = Convert.ToString(multiplier, 2);

    string temp = "";
    for (int i = binaryMultiplier.Length-1, j=0;i >= 0;i--,j++){
        
        if (binaryMultiplier[i]=='1')
        {
            if (string.IsNullOrEmpty(temp))
            {
                temp = binary.PadRight(binary.Length + j, '0');
            } else
            {
                temp = BinaryAdd(temp, binary.PadRight(binary.Length + j, '0'));
            }
        }
    }
    return Convert.ToInt32(temp, 2);
}

static string BinaryAdd(string a, string b)
{
    int carryover = 0;
    StringBuilder stringBuilder = new StringBuilder();
    for (int startA = a.Length - 1, startB = b.Length - 1; startA >= 0 || startB >= 0; startA--, startB--)
    {
        int curA = startA >= 0 ? a[startA] - '0' : 0;
        int curB = startB >= 0 ? b[startB] - '0' : 0;
        int sum = curA + curB + carryover;

        if (sum > 1)
        {
            stringBuilder.Insert(0, sum % 2);
            carryover = 1;
        }
        else
        {
            stringBuilder.Insert(0, sum);
            carryover = 0;
        }
    }
    if (carryover == 1)
    {
        stringBuilder.Insert(0, '1');
    }
    return stringBuilder.ToString();
}