Number Systems
Build an understanding of the binary number system
Terms Used in this Section
| Term | Meaning |
|---|---|
| Binary | Base 2 numbers. |
| Decimal | Base 10 numbers. |
| Hex or Hexadecimal | Base 16 numbers. |
| Place or Place Value | Value of a single number in multi-symbol value. Example: In the number 12345, the Place Value if the 3 is 300. |
| Signed | Numbers that represent negative, zero, and positive values. |
| Symbols | Written characters used to depict numbers. Symbols represent to represent Decimal are 0,1,2,3,4,5,6,7,8,9. |
| Unsigned | Numbers that represent only zero and positive values. |
Introduction
The advent and evolution of number systems were essential to keep pace with human's needs for understanding and classifying the work around us. Creating a common system to show and calculate quantities is the framework or mathematics...and, more specific to our interests, computer science.
In this section, we will review our understanding of the Base 10/Decimal number system as you likely learned in early elementary school.
We will see how a different number system, built on the same rules and constructs learned in primary grades, is best suited for modern computer systems.
And we will learn of a couple of other systems that make it easier for computer scientists to discuss numbers in software and hardware.
First a Review
A brief history of numerical systems - Alessandra King - TED-Ed
1, 2, 3, 4, 5, 6, 7, 8, 9... and 0. With just these ten symbols, we can write any rational number imaginable. But why these particular symbols? Why ten of them? And why do we arrange them the way we do? Alessandra King gives a brief history of numerical systems.
Lesson by Alessandra King, animation by Zedem Media. Copyright CC BY–NC–ND 4.0 International
Decimal Values
Let's start by reviewing some key concepts of the Base 10/Decimal system. Decimal is so engrained in our society, economy, and scientific practices that it is easy to forget the underlying rules that govern it.
Binary Values
The same concepts from the Decimal Number System can be applied to other systems. We will see how, with a basic change to the Base-iness of the system, we can define a different system.
Apply base 10 principles and practices to base 2.
Hexadecimal Values
Understand how base 16 (hex) number system is a shorthand to base 2 (binary).
To get started, expand the section in the Sidebar Menu and read each section