Serialize and Deserialize Binary Tree

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Codec {
private:
    static const int BITS = 12;

public:
    // Encodes a tree to a single string.
    string serialize(TreeNode* root) {
        if (root == nullptr) return string(BITS - 1, '0') + "1";

        string bin = to_binary(root->val);
        bin += serialize(root->left);
        bin += serialize(root->right);

        return bin;
    }

    // Decodes your encoded data to tree.
    TreeNode *deserialize(string data) {
        int idx = 0;
        return deserialize(data, idx);
    }

private:
    TreeNode* deserialize(string &data, int &idx) {
        string bin = data.substr(idx, BITS);
        if (bin == string(BITS - 1, '0') + "1") return nullptr;

        TreeNode *root = new TreeNode(from_binary(bin));

        idx += BITS;
        root->left = deserialize(data, idx);

        idx += BITS;
        root->right = deserialize(data, idx);

        return root;
    }

    string to_binary(int n) {
        bool neg = n < 0;
        n = abs(n);

        string bin = "";
        while (n) {
            int bit = n & 1;
            bin += (char) ('0' + bit);
            n >>= 1;
        }

        while ((int) bin.size() < BITS - 1) {
            bin += '0';
        }

        bin += neg ? '1' : '0';

        return bin;
    }

    int from_binary(string &bin) {
        int val = 0;
        for (int i = 0; i < BITS - 1; i++) {
            if (bin[i] == '1') {
                val |= (1 << i);
            }
        }

        if (bin[BITS - 1] == '1') val = -val;
        return val;
    }
};

// Your Codec object will be instantiated and called as such:
// Codec ser, deser;
// TreeNode* ans = deser.deserialize(ser.serialize(root));