How to Add Binary Numbers

What’s 1 + 1? It’s obviously 2, right? Wrong…at least when we’re talking about binary numbers. How do you add binary numbers? And why is binary addition important in the modern world? Keep on reading to find out!

Jason Marshall, PhD,
February 22, 2013
Episode #143

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How to Add Binary Numbers

What’s 1+1? It’s obviously 2, right? How about 100+10? Well, that’s obviously 110…right? Believe it or not, wrong…at least not when it comes to binary numbers. It can be kind of hard to wrap your head around, but as soon as we move from our cozy decimal numbered world into a world of binary numbers, things can seem a little confusing. But the truth is that binary addition is no harder than decimal addition. And it’s also an incredibly important part of the modern world. How does it work? And why is it so important? (Hint: think computers and calculators!) Stay tuned because those are exactly the topics we’ll be talking about over the next few weeks.

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Recap: What Are Binary Numbers?

Before we get into binary addition, let’s quickly recap what we’ve learned so far about binary numbers. The binary number system uses just the symbols ‘0’ and ‘1’ to represent an infinite number of numbers. To count in binary, start at ‘0,’ continue to ‘1,’ and then—just as we add a new digit after running out of symbols at the number 9 in decimal—in binary we add a new digit to make the binary number ‘10’ that represents the same number of apples, horses, or whatever as the decimal number 2. After ‘10’ apples comes ‘11’ (or 3) apples, then ‘100’ (or 4), then ‘101’ (or 5), ‘110’ (or 6), ‘111’ (or 7), and on and on—each digit represents the next higher power of 2.

If you want more of a refresher about the basics of counting with binary numbers and converting from binary to decimal, I highly encourage you to check out Part 1 and Part 2 of our series called What Are Binary Numbers? before continuing on.


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