Number Bases

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

The Invention of Number Bases

Introducing Binary

Binary on Computers

Exploding Dots


Binary Operations

Perfect Shuffles


Hexadecimal Operations

An Unusual Computer Base


Last Digits Rules

More Divisibility Rules

Cryptograms Solved by Divisibility

Cryptogram Addition Puzzles

Cryptogram Variety Pack

Factorial Refresher

Calculation Tricks

Digital Roots

Terminating Decimals

Repeating Decimals

Repeating Patterns

Problem Solving

Hexadecimal Divisibility Shortcuts (I)

Hexadecimal Divisibility Shortcuts (II)

Hexadecimal Divisibility Shortcuts (III)

Divisibility Shortcuts in Other Bases

Hexadecimal Last Digits

Last Digits in Other Bases

Course description

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.

Topics covered

  • Binary
  • Change of Base
  • Digital Roots
  • Divisibility
  • Hexadecimal
  • Last Digits
  • Perfect Shuffling
  • Repeating Decimals
  • Repunits
  • Terminating Decimals

Prerequisites and next steps

This course assumes prerequisite familiarity with algebra at the level of the Algebra Fundamentals course. Modular arithmetic (which is covered in "Number Theory") also makes an appearance, but is only needed in the last chapter of this course.


  • Number Theory