Code: The Hidden Language of Computer Hardware and Software, First Edition

Chapter 13. But What About Subtraction?

After you’ve convinced yourself that relays can indeed be wired together to add binary numbers, you might ask, “But what about subtraction?” Rest assured that you’re not making a nuisance of yourself by asking questions like this; you’re actually being quite perceptive. Addition and subtraction complement each other in some ways, but the mechanics of the two operations are different. An addition marches consistently from the rightmost column of digits to the leftmost column. Each carry from one column is added to the next column. We don’t carry in subtraction, however; we borrow, and that involves an intrinsically different mechanism—a messy back-and-forth kind of thing.

For example, let’s look at a typical ...