In the previous post, we explored how computers use electrical signals to create binary code—sequences of 0s and 1s that encode all the data and instructions we use. But binary alone isn’t enough to explain how computers perform operations, make decisions, or process information. For that, we need Boolean logic, a system that allows computers to manipulate binary data according to specific rules.
Boolean logic is the foundation of computation. It enables computers to perform everything from simple arithmetic to complex decision-making by combining binary values with logical operations. In this post, we’ll break down what Boolean logic is, how it works, and how it enables computers to represent and process the world.
What Is Boolean Logic?
Long before computers existed, philosophers like Aristotle laid the groundwork for what we now call logic. Aristotle’s system of syllogisms—rules for reasoning about propositions—was one of the first formal methods for evaluating whether statements were true or false.
For example, in Aristotle’s logic, a basic syllogism might look like this:
- Premise 1: All humans are mortal.
- Premise 2: Socrates is a human.
- Conclusion: Therefore, Socrates is mortal.
This method of reasoning uses propositions (statements that are either true or false) and rules to derive conclusions.
In the 19th century, George Boole extended these ideas into a mathematical system that could handle logical operations on binary values (true/false). Boolean logic formalized operations like AND, OR, and NOT, creating the foundation for modern computation. The system revolves around logical operators—functions that combine or modify binary values to produce new results.
The Three Core Logical Operators
1. AND
The AND operator outputs 1 (true) only when both inputs are 1. If either input is 0, the output is 0.
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Example:
- If you have two switches connected in series, electricity will only flow (output = 1) when both switches are closed (inputs = 1).
2. OR
The OR operator outputs 1 if either input is 1. The only time the output is 0 is when both inputs are 0.
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Example:
- If you have two switches connected in parallel, electricity will flow (output = 1) if either switch is closed (input = 1).
3. NOT
The NOT operator takes a single input and inverts it. If the input is 1, the output is 0; if the input is 0, the output is 1.
| Input | Output |
|---|---|
| 0 | 1 |
| 1 | 0 |
Example:
- Think of a NOT operator as a light switch that toggles the light’s state. If the light is off (input = 0), flipping the switch turns it on (output = 1), and vice versa.
Boolean Logic in Action: Representing the World
🛠️ … in progress … 🛠️
Conclusion: The Power of Logical Rules
Boolean logic transforms binary code into a tool for computation. By combining simple logical rules, computers can make decisions, execute programs, and represent real-world scenarios in binary form.
In the next post, we’ll explore how memory works and how computers use these logical operations to store and retrieve data, enabling them to perform tasks and remember information.