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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.

Interactive
quizzes

29

Concepts and
exercises

235+
  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.

    1. Included with
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      Exploding Dots

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

    2. Included with
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      Binary

      Convert between base 2 and base 10.

    3. Included with
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      Binary Operations

      Add, subtract, and multiply directly in binary.

    4. Included with
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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.

    1. Included with
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      Divisibility

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

    2. Included with
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      Last Digits Rules

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

    3. Included with
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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.

    4. Included with
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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.

    1. Included with
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      Factorial Refresher

      Check your knowledge of the ! symbol in mathematics.

    2. Included with
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      Calculation Tricks

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

    3. Included with
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      Digital Roots

      Investigate surprising patterns that surface when you calculate digital roots.

    4. Included with
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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?

    1. Included with
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      Hexadecimal Divisibility Shortcuts (I)

      Learn some number theory tricks that work in hexadecimal.

    2. Included with
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      Hexadecimal Divisibility Shortcuts (II)

      Continue adding to your repertoire of hexadecimal divisibility tricks.

    3. Included with
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      Hexadecimal Divisibility Shortcuts (III)

      Discover a divisibility test that uses an alternating sum.

    4. Included with
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      Divisibility Shortcuts in Other Bases

      Apply what you've learned about divisibility tricks to unusual bases like 6 and 12.