At its heart, the logic that powers all of our digital devices is surprisingly simple. It's based on a single, fundamental idea: everything can be in one of two possible states. Think of a light switch. It can be ON, or it can be OFF. There's no in-between. This is the core of binary logic.

In this system, we don't deal with shades of gray. A statement is either completely TRUE or completely FALSE. This simplifies complex problems into a series of yes-or-no questions.

To make this system work for computers, we represent these two states with numbers: 1 and 0.

• 1 represents TRUE, or ON.
• 0 represents FALSE, or OFF.

Every piece of information in a computer, from the text you're reading to a complex video game, is built from these simple ones and zeroes. A variable that can only hold one of these two values is called a binary variable.

The world we experience every day is mostly analog. Think of a dimmer switch for a light. You can slide it smoothly to get any level of brightness, from completely dark to fully lit, and countless levels in between. An analog signal has a continuous range of values.

Digital systems, like computers, work differently. They break everything down into discrete, separate steps. Instead of a dimmer, a digital system uses a simple ON/OFF switch. This binary approach is much less ambiguous. A signal is clearly a 1 or a 0, which makes it incredibly reliable for storing and processing information.

Understanding this simple two-state world is the first step in mastering Boolean algebra. Everything else we'll learn is built on this foundation of 1s and 0s.