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What Is Boolean Algebra?

What is Boolean algebra? Is it as complicated as it sounds? Why is it so important in the day-to-day functioning of the modern world? Keep on reading to find out!

By
Jason Marshall, PhD,
Episode #144

What Is Boolean Algebra?

Today we’re going to talk about one of those topics in math that sounds incredibly hard but is actually pretty straightforward: Boolean algebra. Sounds painful, right? Well, as you’ll soon see, it isn’t. Plus, the simple ideas behind Boolean algebra are actually something you’re most likely already familiar with…you just don’t know it yet! And it turns out that these ideas are some of the most important bits of math that you use in your day-to-day life. So, how does Boolean algebra work? And when do you use it? Stay tuned because those are exactly the questions we’ll be talking about today..

How Do Computers Add?

If you’ve been following along for the past few weeks, you know that we’ve been on something of a quest. We started by talking about the basics of counting in binary, we then talked about some tricks that thinking in binary make possible, and last week we learned how to perform binary addition. What do these topics have in common? Obviously, they’re all about binary numbers. While binary numbers are certainly fun and interesting in their own right, they aren’t actually what we’ve been questing for. Instead, our goal is to understand the math that allows an inanimate object like a calculator to perform the rather intelligent task of adding two numbers—a feat which binary numbers play a key role in.

Similarly, while today’s topic—Boolean algebra—is perfectly interesting in its own right, keep in mind that our main goal is to ultimately understand the math that allows computers and calculators to do addition. And in order to do that, we need to first figure out what we can do with Boolean algebra.

What Is Boolean Algebra?

So, what is Boolean algebra? Well, for our purposes, we can think of Boolean algebra as a type of math that deals with bits instead of numbers. What does that mean? Well, as we’ve learned, a bit (which is shorthand for “binary digit”) can have a value of either 1 or 0. In Boolean algebra, a binary value of 1 is interpreted to mean “true” and a binary value of 0 means “false.” Which means that Boolean algebra can equivalently be thought of as a particular type of math that deals with true and false values—aka truth values—instead of numbers. What kind of things can we do to these truth values?

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