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# Number Bases

## Master the fundamentals for working in decimal, binary, hexadecimal, and other bases.

It's a traditional choice to use base ten by default. You see the numerical digits 0-9 every day and you probably find it most natural to use base 10, even if you already know about binary and hexadecimal. However, many concepts in math and applications in computer science are more simply and elegantly expressed in non-decimal bases.

This course introduces a variety of powerful tools for problem-solving that take advantage of knowing and controlling what number base you're working in. You'll learn techniques for doing math in many different bases and explore applications to computer science, magic card tricks, and advanced, abstract math.

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1. 1

### Introduction

Learn about the positional base system and the impact it has on computer systems.

1. #### The Invention of Number Bases

What's the difference between an additive system and a positional system?

2. #### Introducing Binary

Learn how to write any number using only 1s and 0s.

3. #### Binary on Computers

Apply your skill with binary to real scenarios in computer science.

2. 2

### Binary and Other Bases

Study base 2, base 16, and one other base that is at the frontier of computer technology.

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#### Exploding Dots

Connect the game of exploding dots with the number base system.

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#### Binary

Convert between base 2 and base 10.

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#### Binary Operations

Add, subtract, and multiply directly in binary.

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#### Perfect Shuffles

Apply binary to decipher the magic behind card shuffling.

3. 3

### Digits and Divisibility

Establish and explore patterns related to digit placement and divisibility.

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#### Divisibility

Apply the divisibility rules for 1, 2, 5, and 10, and summarize why this set is special.

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#### Last Digits Rules

What's different about the divisibility rules for 4 and 8?

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#### More Divisibility Rules

The rules for 3, 6, 7, and 9, are a fair bit stranger than what you've seen so far.

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#### Cryptograms Solved By Divisibility

Apply your understanding of divisibility rules to cracking cryptogram puzzles!

4. 4

### Decimal Expansions in Base 10

The standard base 10 system itself holds some mysteries that you'll unlock here.

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#### Factorial Refresher

Check your knowledge of the ! symbol in mathematics.

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#### Calculation Tricks

Perform arithmetic in situations where there's a shortcut method.

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#### Digital Roots

Investigate surprising patterns that surface when you calculate digital roots.

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#### Terminating Decimals

When do fractions terminate when changed into decimal form?

5. 5

### Divisibility in Other Bases

What happens to divisibility tests when the base is no longer 10?

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Learn some number theory tricks that work in hexadecimal.

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