Book Image

Practical Discrete Mathematics

By : Ryan T. White, Archana Tikayat Ray
Book Image

Practical Discrete Mathematics

By: Ryan T. White, Archana Tikayat Ray

Overview of this book

Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you’ll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you’ll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you’ll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
Table of Contents (17 chapters)
1
Part I – Basic Concepts of Discrete Math
7
Part II – Implementing Discrete Mathematics in Data and Computer Science
12
Part III – Real-World Applications of Discrete Mathematics

Hexadecimal numbers and their application

In this section, we will learn about the hexadecimal number system and its application. We use hexadecimal numbers in our day-to-day lives without realizing, such as for the MAC address of your phone or computer.

Hexadecimal numbers are base-16 numbers. They can be represented by using 10 digits (0 to 9) and 6 letters (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15).

Let's look at some conversions between the decimal and hexadecimal number systems:

Figure 3.15 – Counting in hexadecimal

Just like decimal numbers, hexadecimal numbers also have place values:

(100)16 = (1 ∙ 162) + (0 ∙ 161) + (0 ∙ 160) = 256

Computer programmers use hexadecimal numbers to simplify the binary number system. We know that 24 = 16, so we know there is a linear relationship between 2 and 16, which implies that four binary digits would be equivalent to one hexadecimal digit. In other words, since...