What Are Binary Numbers? Part 1

How do binary numbers work? How do you count in binary? And how can you use binary numbers to quickly guess a number between 1 and 1,000? Keep on reading to find out!

Jason Marshall, PhD
5-minute read
Episode #141

Quick, think of a number between 1 and 1,000. If I was to tell you that I can figure out your number in no more than 10 guesses, would you believe me? Absolutely not! After all, I’d just be guessing randomly, so it’s usually going to take me a lot longer to figure out your number…probably hundreds of guesses.

But what if every time I guess your number you agree to tell me if it’s higher or lower than my guess? Is that enough information for me to figure out your number in 10 or fewer guesses? Believe it or not, it is! How does it work? And what does all of this have to do with the binary numbers computers use? Stay tuned because those are precisely the questions we’ll be answering over the next few weeks..

What Are Binary Numbers?

Before we can harness the power of binary numbers to turn you into a number-guessing magician, we first need to figure out what the binary number system is and how it works. The good news is that the binary number system is literally the simplest number system you can imagine. What exactly do I mean by that? Well, as you know, the decimal system that we all know and love uses ten different symbols—0 through 9—to construct all possible numbers. In contrast, the binary system uses only two symbols—0 and 1—to do the same thing.

See, it’s much simpler! But how is this possible? It seems as if there must be things we can do with ten symbols than we can’t do with only two, right? Well, let’s think about that. In particular, let’s think about whether or not we can count up to any arbitrarily large number using only the symbols 0 and 1.


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.