Number Base Systems - Mathematics (Senior Secondary)

This course provides a complete study of number base systems, a core concept in mathematics and computer science. It moves beyond the familiar base 10 system to explore how numbers are represented and manipulated in other bases, such as binary, which forms the foundation of all digital technology. We will cover the principles of different bases, methods for conversion between them, and arithmetic operations within these systems. A command of number bases is non-negotiable for anyone serious about computer science or digital electronics. It is the language of computers. This knowledge is essential for understanding data representation, low-level programming, and network protocols. It provides a deeper appreciation for the structure of the number system we use every day. By the end of this course, you will be able to convert any number from one base to another, including decimal fractions. You will perform addition, subtraction, multiplication, and division in any base with confidence. You will also explain the direct application of the binary system in computer programming. This course is built for secondary school students taking their first formal steps into advanced mathematical concepts. It is also essential for aspiring programmers, computer science students, and electronics enthusiasts who need to understand the fundamental principles of digital systems. No prior knowledge beyond basic arithmetic is required.

Enrolment valid for 12 months

Course Chapters

1. Introduction

This chapter sets the foundation for the course. We will define what a number base is and explain why studying systems beyond the standard base 10 is a critical skill in a technology-driven world. By the end of this chapter, you will understand the course objectives. You will learn the structure of different number bases and recognise their importance in mathematics and computer science.

Chapter lessons

1-1. Welcome

This lesson outlines the course structure and objectives. We will define what a number base is and establish the practical skills you will gain.

1-2. Why number bases?

This lesson explains the practical importance of studying number bases. We focus on the role of the binary system in powering all modern digital technology.

2. Conversions

This chapter covers the essential mechanics of working with different number bases. We will focus on the systematic processes for converting numbers between the decimal system and other bases. By the end of this chapter, you will master the methods for converting from other bases to base 10. You will also learn to convert from base 10 to other bases and handle decimal fractions.

Chapter lessons

2-1. Converting from other bases to base 10

This lesson teaches the expansion method for converting numbers into the standard base 10 system. This is a foundational skill for all subsequent conversions.

2-2. Converting from base 10 to other bases

This lesson demonstrates the method of repeated division. You will learn to convert any base 10 integer into an equivalent representation in another base.

2-3. Converting decimal fractions in one base to another

This lesson addresses the conversion of fractional numbers between bases. We will cover the specific techniques required for handling the decimal component accurately.

3. Arithmetic in Other Bases

This chapter moves from conversion to calculation. We will apply standard arithmetic operations - addition, subtraction, multiplication, and division - within non-decimal number systems. By the end of this chapter, you will be able to perform all four basic arithmetic operations in any number base. You will solve complex problems without first converting to base 10.

Chapter lessons

3-1. Addition and subtraction

This lesson covers the rules for addition and subtraction in other bases. We will focus on the process of borrowing and carrying over within different systems.

3-2. Multiplication and division

This lesson teaches the methods for multiplication and division in any number base. You will apply these skills to solve arithmetic problems directly.

4. Applications

This chapter connects theory to practice. We will explore the primary real-world application of number base systems, focusing on its central role in computing. By the end of this chapter, you will understand how number base theory is applied. You will be able to explain the specific importance of the binary system.

Chapter lessons

4-1. Application of number bases to computer programming

This lesson demonstrates how the binary (base 2) system forms the fundamental language of computers. We will connect number base theory to practical technology.

5. Conclusion and Next Steps

This concluding chapter summarises the core skills you have acquired in the course. It solidifies your understanding and provides a clear direction for what to learn next. By the end of this chapter, you will have reviewed the key concepts of number bases, conversions, and arithmetic. You will also understand how this knowledge connects to other areas of mathematics.

Chapter lessons

5-1. Summary of what you have learned

This lesson provides a concise review of the entire course. We will cover conversions, arithmetic operations, and the practical application of number systems.

5-2. How number bases relate to advanced mathematics

This lesson places your new skills in a broader context. It shows how a firm grasp of number bases is essential for topics in discrete mathematics and computer science.