Have you ever wondered how computers and calculators—both of which are nothing more than mindless boxes of plastic, wires, and other strange parts—manage to add numbers? And so quickly! Math Dude has the answer.
Have you ever wondered how computers and calculators—both of which are nothing more than mindless boxes of plastic, wires, and other strange parts—manage to do something as intelligent as add numbers? And so quickly at that! How do they do it? And what does it have to do with the binary numbers and Boolean algebra we’ve been talking about lately? Stay tuned because those are exactly the questions we’ll be answering over the next few weeks..
Review: Boolean Algebra
For the past few weeks we’ve been trying to figure out how computers and calculators add. We started by talking about the binary number system, we then talked about some binary number tricks and how to perform binary addition, and then we talked about something called Boolean algebra. The first important thing to remember about Boolean algebra is that it’s a type of math that deals with bits instead of numbers like you’re used to. What’s a bit? It’s simply a binary digit, and it can be equal to 1 (aka, “true”) or 0 (aka, “false”), and nothing else.
The second important thing to remember about Boolean algebra is its 3 fundamental operations: AND, OR, and NOT. What do they do? Well, NOT simply gives you back the opposite value of the bit you give it. So NOT 0 is equal to 1 and NOT 1 is equal to 0. AND and OR both take the values of two bits and give you back 1 or 0. AND gives you 1 back only if both input bits are equal to 1, and OR gives you 1 back if either (or both) input bits are equal to 1. Amazingly, these three operations—NOT, AND, and OR—are the keys to understanding how computers add.