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

Converting between bases

Now that we have the basic knowledge about base-n numbers, let's move on and see how these numbers transform between different bases. We can transform numbers in any base to base-10 and vice versa. In this section, we will show the conversion between different bases along with examples and Python code.

Converting base-n numbers to decimal numbers

Using the definition of base-n numbers given previously, we can convert the following numbers to base-10, or decimal, form. Several examples follow:

  • (a)n = a ∙ n0 = a
  • (ab)n = a ∙ n1 + b ∙ n0 = an + b
  • (abc)n = a ∙ n2 + b ∙ n1 + c ∙ n0 = an2 + bn + c
  • (abcd)n = a ∙ n3 + b ∙ n2 + c ∙ n1 + d ∙ n0 = an3 + bn2 + cn + d

We can apply this according to the number of digits we have.

Example – Decimal value of a base-6 number

Let's convert the number (3214)6 into decimal form for this example:

(3214...