Add Binary

Given two binary strings, return their sum (also a binary string).

For example,
a = "11"
b = "1"
Return "100".

#include<iostream>
#include<string>
#include<vector>

using namespace std;

string addBinary(string a, string b) {
	if (a.empty()||b.empty())
		return a.empty()?b:a;

	int idx_a = a.size()-1,idx_b = b.size()-1; 
	int length = max(idx_a,idx_b)+1;
	string Result;
	int add =0;
	for (;idx_a>=0&&idx_b>=0;--idx_a,--idx_b)
	{
		int num = a[idx_a]-'0'+b[idx_b]-'0'+add;
		add  = num/2;
		num %= 2;
		Result = static_cast<char>(num+'0')+Result;
	}
	while (idx_a>=0)
	{
		int num = a[idx_a]-'0'+add;
		add  = num/2;
		num %= 2;
		Result = static_cast<char>(num+'0')+Result;
		idx_a--;
	}
	while (idx_b>=0)
	{
		int num = b[idx_b]-'0'+add;
		add  = num/2;
		num %= 2;
		Result = static_cast<char>(num+'0')+Result;
		idx_b--;
	}
	if (add>0)
		Result = static_cast<char>(add+'0')+Result;
	return Result;
}