Boolean Logic Explained: AND, OR, NOT for Beginners

Whether you realize it or not, you use Boolean logic daily. By saying "I do NOT want that" or "I like this AND that," you use Boolean expressions.

Boolean logic (and binary logic) is considered true/false logic. For example, if someone asked you if you like ice cream, if you were using Boolean logic, you could say "yes" or "no" (yes being true and no being false). A few operators commonly used for boolean operations are NOT, AND, and OR.

Let's dive into the basics of Boolean logic for beginners.

The Three Most Important Boolean Operators

Boolean operations are the foundation of logic in digital computers and everyday decisions. The three most basic and important Boolean operations are AND, OR, and NOT.

AND Operator

The AND operation checks if two or more conditions are true. If every input is true, the output will also be true. If even one of the inputs is false, the entire statement becomes false. Consider this statement:

If I like ice cream AND cake, then I like ice cream cake.

Both conditions, liking ice cream and liking cake, must be true for the conclusion to be true. If you like only one of the two, the statement becomes false. In Boolean logic, this would look like:

This table is called a truth table. The truth table for the AND operator shows that only when both A and B are 1 (true) does the output become 1.

OR Operator

The OR operation checks if at least one of the conditions is true. If either one (or both) inputs are true, the output will also be true. It only becomes false when both inputs are false. As an example:

If I like cookies OR brownies, then I'll be happy.

Even if you like just one of them, you'll still be happy. The only way you wouldn't be happy is if you didn't like either. Truth table for OR:

NOT Operator

The NOT operation is a bit different—it's a unary operator, meaning it works with only one input. NOT is the smallest of the Boolean logic operators. The NOT operation simply inverts the value it receives as input. If the input is true, it outputs false. If the input is false, it outputs true.

If I do not like broccoli, then I won't eat it.

Here, liking broccoli is the input. The NOT operator flips that value. If you do like it (true), the NOT turns it into false (you won't avoid it). If you don't like it (false), the NOT turns it into true (you'll avoid it). The truth table for NOT is much simpler compared to AND and OR, because it has only one input:

If-Then Logic Format

Most Boolean operations can be described using an "if-then" format. These statements form the basic logic we use in everyday decisions and programming. For example:

If it's raining AND I forgot my umbrella, then I'll get wet.

This is a Boolean condition: two truths lead to a logical consequence. In digital computers, computing with logic gates, millions of decisions are made every second, all using this Boolean format.

Common Extra Symbols

In Boolean logic, a common symbol is a line over an operator, which looks like this: W̅. This means to perform the "not" operation on the value W. So if W equals 1, W̅ equals 0. This is one of the most common Boolean logic symbols in many circuit applications.

You may also see a truth table that looks like this:

The "X" in this context means that if Input A is a zero, we "don't care" about Input B or the Output.

A common example of when to use this "don't care" is when something has an enable input. If the enable input (Input A in this context) is "off" then the whole circuit should be turned off as well, making Input B and the Output irrelevant.

Conclusion

Boolean logic, using just 3 operators, has many applications in circuits and in speech. Understanding Boolean logic as a beginner is important in your journey to understanding electronics as a whole.

Boolean logic forms the backbone of programming, digital electronics, and computer science. By mastering the fundamental Boolean operators, you'll be ready to explore more advanced topics like logic gates and digital circuits.