Module 3: Numeration Systems

Learning Objectives

Describe historical examples of simple grouping, multiplicative grouping, and positional numeration systems in the development of modern mathematics.
Write and interpret numbers in other bases.
Convert directly between binary, octal, decimal, and hexadecimal bases.
Recognize when use of other bases is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others.

Reading Notes: Historical Counting Systems

Introduction and Basic Number and Counting Systems
As we begin our journey through the history of mathematics, one question to be asked is “Where do we start?” Depending on how you view mathematics or numbers, you could choose any of a number of launching points from which to begin.

Videos: Historical Number Systems

Please watch these videos in the order presented.

Reading Notes: Binary, Octal, and Hexadecimal

Binary, Octal, and Hexadecimal
In modern computing and digital electronics, the most commonly used bases are decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). If we are converting between two bases other than decimal, we typically have to convert the number to base 10 first, and then convert that number to the second base. However, we can easily convert directly from binary to octal, and vice versa, and from binary to hexadecimal, and vice versa.

Videos: Binary, Octal, and Hexadecimal

Screenshot for the video, Pre-Algebra 3 - Decimal, Binary, Octal & Hexadecimal (rev 2). Click the image to watch the movie. A new window will open.

Screenshot for the video, Binary, Hexadecimal, Octal conversion. Click the image to watch the movie. A new window will open.

Optional Project: Application of numeration in real life

Application of Numeration in Real Life
This assignment will help you practice applying what you have learned about numeration systems to real problems or situations, and communicating about mathematical ideas with others.

Assessment: Numeration Systems

Complete this assessment after you finish all sections in Module 3.

Assessment: Numeration System

Licenses & Attributions

CC Licensed Content, Original Content

Application of Numeration in Real Life. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.

CC Licensed Content, Shared Previously

Historical Counting Systems. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.
Intro to bases - converting base 7 to base 10. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Converting base 10 to base 5. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Converting base 10 to base 7 using remainder. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Converting base 10 to base 5 using calculator method. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Bases over 10, intro to Mayan numbers. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Converting a Mayan number to base 10. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Converting base 10 to a Mayan number. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Adding Mayan numbers. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Binary and hexadecimal systems. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.
Binary, Octal, and Hexadecimal. Found in: Introduction to College Mathematics. Provided by: Lumen Learning. License: CC BY 4.0 except where otherwise noted.
Assessment: Numeration System – Questions. Authored by: David Lippman, Lawrence Morales, and James Sousa. License: IMathAS Community License (GPL + CC-BY).

Pre-Algebra 3 - Decimal, Binary, Octal & Hexadecimal. Authored by: MyWhyU. Located at: https://youtu.be/5sS7w-CMHkU. License: All Rights Reserved. License Terms: Standard YouTube License.

MAT 100 - Introduction to College Mathematics - Textbook

License & Attribution

MAT 100 Introduction to College Mathematics

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