For almost the last 20 years, an Apple laptop of one variety or another has been my main computing device. Imagine my surprise when I finally learned today that Apple keyboards don’t have an Insert key. In almost two decades I have never needed it, but that changed this morning.
While working in my favorite Python editor, Wing IDE by Wingware, some sloppy touch typing resulted in the cursor changing from the blinking vertical line I am used to a blinking underline. That change was subtle enough that I missed it, but as soon as I began typing and the text I was entering started overwriting the existing code, I knew something was up. WTF!
Abraham Lincoln once famously said, “Everybody loves a compliment.” I suspect that if he had been a mathematician he would have loved complements, too. We’ve already seen what complements are and talked about the two most prolific: the radix complement and the diminished radix complement. Now it’s time to explore how we can leverage complements to do some really interesting integer arithmetic. Using complements we can subtract one positive integer from another or add a negative integer to a positive one by simply performing addition with two positive integers. The algorithm behind this black magic is called the Method of Complements.
