Review of number bases - SS3 ICT Lesson Note

Number bases, also known as numeral systems, are fundamental concepts in mathematics and computer science that play a crucial role in representing and manipulating numerical information. The four most commonly used number bases are binary, octal, decimal, and hexadecimal.

Binary (Base 2):

Base: Binary is a base-2 numeral system, meaning it uses only two digits, 0 and 1.
Representation: In binary, each digit represents a power of 2, with the rightmost digit being 2⁰ (1), the next being 2¹ (2), the next 2² (4), and so on.
Usage: Binary is fundamental in digital electronics and computing, where it represents the on/off state of electronic components.

Octal (Base 8):

Base: Octal is a base-8 numeral system, using digits 0 through 7.
Representation: Each digit in octal represents a power of 8, similar to how each digit in decimal represents a power of 10.
Usage: Octal is less commonly used today but was more prevalent in early computing. It is sometimes used in permissions systems in Unix-like operating systems.

Decimal (Base 10):

Base: Decimal is the most common numeral system worldwide, with ten digits (0 through 9).
Representation: Each digit represents a power of 10, with the rightmost digit being 10⁰ (1), the next 10¹ (10), the next 10² (100), and so forth.
Usage: Decimal is used in everyday arithmetic and mathematics, making it the default number system for most human calculations.

Hexadecimal (Base 16):

Base: Hexadecimal is a base-16 numeral system, using digits 0-9 and letters A-F (or a-f) to represent values 10-15.
Representation: Each digit in hexadecimal represents a power of 16, with the rightmost digit being 16⁰ (1), the next 16¹ (16), the next 16² (256), and so on.
Usage: Hexadecimal is widely used in computing, especially in low-level programming, as it provides a more concise representation of binary data. It's commonly used for memory addresses, color codes, and debugging.

In summary, each number base has its unique characteristics and applications:

Binary is fundamental in digital systems.
Octal is less common but historically used in computing.
Decimal is the everyday base for human calculations.
Hexadecimal is crucial in computer science and programming for its concise representation of binary data.