Master the fundamentals for working in decimal, binary, hexadecimal, and other bases.
The Invention of Number Bases
Binary on Computers
An Unusual Computer Base
Last Digits Rules
More Divisibility Rules
Cryptograms Solved By Divisibility
Cryptogram Addition Puzzles
Cryptogram Variety Pack
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
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.
- Change of Base
- Digital Roots
- Last Digits
- Perfect Shuffling
- Repeating Decimals
- 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.