March 2026
Intermediate
512 pages
14h 19m
English
Content preview from Mathematics in Cybersecurity
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3Introduction to Number Systems
In this chapter, we will explore the important world of number systems, focusing on binary and other commonly used number systems in mathematics, cybersecurity, information systems, and computer science. We will begin by defining a number system and expressing why it is crucial in these fields.
3.1 What Is a Number System?
A number system is a way of representing numbers using a set of symbols called digits. The most familiar number system is the decimal system, which uses 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, there are many other number systems, each with its own set of digits and rules for representing and manipulating numbers.
The number of digits used in a particular number system is called its base or radix. For example, the decimal system is a base-10 system because it uses 10 digits. Other common number systems include:
- Binary (base-2): Uses digits 0 and 1.
- Octal (base-8): Uses digits 0, 1, 2, 3, 4, 5, 6, and 7.
- Hexadecimal (base-16): Uses digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and letters A, B, C, D, E, and F to represent values 10 through 15.
At this point, it is not expected that you recognize the binary, octal, and hexadecimal representations of the decimal number 42; this will be made clear shortly. As we shall see, understanding the various representations involves ...
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