def add_binary(Input1: str, Input2: str) -> str:
    Result = []
    Initially = 0
    i, j = len(Input1) - 1, len(Input2) - 1
    
    while i >= 0 or j >= 0 or Initially:
        total_sum = Initially
        if i >= 0:
            total_sum += int(Input1[i])
            i -= 1
        if j >= 0:
            total_sum += int(Input2[j])
            j -= 1
        
        Initially = total_sum // 2
        Result.append(str(total_sum % 2))
    
    return ''.join(Result[::-1])

# Example usage:
Input1 = "11"
Input2 = "1"
print("Example_1 : " + add_binary(Input1, Input2))

Input1 = "1010"
Input2 = "1011"
print("Example_2 : " + add_binary(Input1, Input2))