5.2 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
Binary Operations
Perfect Shuffles
Hexadecimal
Hexadecimal Operations
An Unusual Computer Base
Divisibility
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.