Different Ways to Count
A comprehensive guide to number systems for high school students with STEM/STEAM experience.
About This Book
Have you ever wondered why there are 60 seconds in a minute? Why programmers talk about “hexadecimal”? Why we use base-10 when base-12 might be better?
This book explores the fascinating world of different counting systems—from the binary code that powers your computer to the ancient Babylonian mathematics that still governs how we tell time.
What You’ll Learn
- Base-10 (Decimal): Why our familiar system works the way it does—and its surprising limitations
- Base-2 (Binary): The fundamental language of all computers and digital devices
- Base-8 (Octal): The forgotten shorthand that once dominated computing
- **Base-16 (Hexa…
Different Ways to Count
A comprehensive guide to number systems for high school students with STEM/STEAM experience.
About This Book
Have you ever wondered why there are 60 seconds in a minute? Why programmers talk about “hexadecimal”? Why we use base-10 when base-12 might be better?
This book explores the fascinating world of different counting systems—from the binary code that powers your computer to the ancient Babylonian mathematics that still governs how we tell time.
What You’ll Learn
- Base-10 (Decimal): Why our familiar system works the way it does—and its surprising limitations
- Base-2 (Binary): The fundamental language of all computers and digital devices
- Base-8 (Octal): The forgotten shorthand that once dominated computing
- Base-16 (Hexadecimal): Why programmers see #FF5733 as a color and 0xDEADBEEF as perfectly normal
- Base-12 (Duodecimal): The ancient system that almost won, and why it’s mathematically superior
- Base-60 (Sexagesimal): The 4,000-year-old Babylonian legacy you use every single day
- Other Bases: From Mayan base-20 to base-64 encoding, plus Roman numerals and non-positional systems
Who This Book Is For
This book is designed for high school students who:
- Have some STEM/STEAM experience
- Are curious about mathematics and computer science
- Want to understand how computers really work
- Enjoy learning about history and culture
- Are ready to have their minds slightly bent
No advanced math required—just curiosity and a willingness to see numbers in a new way.
Table of Contents
- Introduction: Why Counting Isn’t as Simple as 1, 2, 3
- Chapter 1: Base-10 (Decimal) — The System You Never Knew You Chose
- Chapter 2: Base-2 (Binary) — The Language of Computers
- Chapter 3: Base-8 (Octal) — The Forgotten Middle Child
- Chapter 4: Base-16 (Hexadecimal) — Programmer’s Best Friend
- Chapter 5: Base-12 (Duodecimal) — Ancient Wisdom
- Chapter 6: Base-60 (Sexagesimal) — The Babylonian Legacy
- Chapter 7: Other Bases and Practical Applications — The Variety Show
- Chapter 8: Conclusion — Counting the Ways
How to Use This Book
Reading Order
The chapters build on each other, so reading in order is recommended. However, if you’re already comfortable with number systems, feel free to skip to chapters that interest you most.
Reading Experience
Settle in with your favorite reading spot. This book is designed to be read and enjoyed, with clear explanations and engaging examples throughout. Let the concepts sink in at your own pace.
Key Features
- Verbose and thorough: Each topic is explored in depth with multiple examples
- Engaging narrative: Educational but entertaining, with humor and cultural context
- Practical applications: Real-world uses from computer science to ancient astronomy
- Historical perspective: Learn why different civilizations chose different bases
- Modern relevance: Understand the technology you use every day
What Makes This Book Different
Unlike typical math textbooks, this book:
- Explains the why, not just the how
- Connects mathematics to history, culture, and technology
- Uses an engaging, conversational tone
- Includes programmer humor and cultural references
- Treats you like an intelligent reader, not a passive student
- Shows that there’s no “best” number system—context matters
Sample Topics You’ll Explore
- Why “10” means different things in different bases
- How to count to 1,023 on your fingers using binary
- Why programmers love the number 0xDEADBEEF
- The real reason there are 360 degrees in a circle
- How to read Unix file permissions (chmod 755)
- What color #FF6347 represents (and why)
- Why the Babylonians were mathematical geniuses
- How computers store negative numbers
- Why Roman numerals dominated for over 1,000 years—and why they failed
- The Dozenal Society’s campaign to replace base-10
Prerequisites
- Basic arithmetic (addition, subtraction, multiplication, division)
- Understanding of exponents (2³ = 8)
- Curiosity about how things work
- Willingness to think differently
Beyond This Book
After completing this book, you’ll be prepared to:
- Understand hexadecimal debugging output
- Work with binary and hexadecimal in programming
- Appreciate ancient mathematical achievements
- Debug computer systems at a lower level
- Think flexibly about representations and systems
Contributing
Found a typo? Have a suggestion? Want to add examples or expand on topics? Contributions are welcome! Please open an issue or submit a pull request.
License
This work is dedicated to students everywhere who’ve asked “but why?” and weren’t satisfied with “because that’s how it is.”
Author’s Note
This book was written to fundamentally change how you think about counting. By the end, you’ll realize that the way you’ve counted your entire life is just one of many possible systems—each with its own logic, history, and purpose.
Numbers don’t change, but our ways of representing them reveal deep truths about mathematics, culture, and human cognition.
Ready to begin? Start with the Introduction.
“There are 10 types of people in the world: those who understand binary, and those who don’t.”
— Anonymous (now you’ll get the joke)