Half adders can't really do any more than this, but if we put a few more logic gates together, we can make what's called a full adder circuit that does harder sums with bigger numbers. How does an adder work? That's beyond the scope of this introductory article, but you can find ...
Adder (electronics): This more detailed (and less clear) article from Wikipedia explains how different logic gates can be used to add numbers in circuits called half adders, full adders, and more complex variations such as ripple-carry adders.Books...