How to manipulate and represent binary numbers in C++

I'm currently trying to build a lookup table for a huffman tree using a pretty simple preorder traversal algorithm, but I'm getting stuck carrying out very basic bit wise operations. The psuedo code follows:

void preOrder(huffNode *node, int bit) //not sure how to represent bit
{
  if (node == NULL)
    return;

  (1) bit = bit + 0; //I basically want to add a 0 onto this number (01 would go to 010)
  preOrder(node->getLeft(), bit);
  (2) bit = bit - 0 + 1; //This should subtract the last 0 and add a 1 (010 would go to 011)
  preOrder(node->getRight());


}

I'm getting quite confused about how to carry out the operations defined on lines (1) and (2)

What data type type does one use to represent and print binary numbers? In the above example I have the number represented as an int, but i'm pretty sure that that is incorrect. Also how do you add or subtract values? I understand how & and | types logic works, but I'm getting confused as to how one carries out these sorts of operations in code.

Could anyone post some very simple examples?