BAB 1 Sistem Bilangan | Matematika Dasar | Alternatifa

Introduction

This tutorial is designed to help you understand the basics of number systems, a fundamental concept in mathematics. Understanding different number systems is crucial for various applications in computer science, programming, and advanced mathematics. In this guide, we will explore the key elements of number systems covered in the video by Alternatifa.Project.

Step 1: Understanding Number Systems

• A number system is a mathematical notation for representing numbers of a given set, using digits or other symbols.

The most common number systems include

• Decimal (base 10)
• Binary (base 2)
• Octal (base 8)
• Hexadecimal (base 16)

Practical Advice

Familiarize yourself with how numbers are represented in each system. For example, the decimal number 10 is represented as

• Binary: 1010
• Octal: 12
• Hexadecimal: A

Step 2: Exploring the Decimal System

• The decimal system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Each digit's position represents a power of 10.

Key Points

• The rightmost digit represents (10^0) (1s place).
• The next digit to the left represents (10^1) (10s place), and so forth.
• Example: The number 345 represents (3 \times 10^2 + 4 \times 10^1 + 5 \times 10^0).

Step 3: Understanding the Binary System

• The binary system uses two digits: 0 and 1.
• Each position represents a power of 2.

Practical Advice

• To convert a binary number to decimal, sum the products of each digit and its corresponding power of 2.

Example: The binary number 1101 represents

• (1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 8 + 4 + 0 + 1 = 13).

Step 4: Learning the Octal System

• The octal system uses eight digits: 0 to 7.
• Each position represents a power of 8.

Key Points

• To convert octal to decimal, multiply each digit by its corresponding power of 8.

Example: The octal number 17 represents

• (1 \times 8^1 + 7 \times 8^0 = 8 + 7 = 15).

Step 5: Exploring the Hexadecimal System

• The hexadecimal system uses sixteen symbols: 0-9 and A-F (where A=10, B=11, ..., F=15).
• Each position represents a power of 16.

Practical Advice

• To convert hexadecimal to decimal, multiply each digit by its corresponding power of 16.

Example: The hexadecimal number 1A3 represents

• (1 \times 16^2 + A (10) \times 16^1 + 3 \times 16^0 = 256 + 160 + 3 = 419).

Conclusion

Understanding different number systems is essential for various fields, including computer science and programming. By mastering how to convert between these systems, you can enhance your mathematical skills and apply them in real-world scenarios. Consider practicing conversions and exploring further applications of these number systems in programming languages or algorithms.