Number System

About

Number systems are methods for representing numbers in a consistent manner. They are essential for various fields, including mathematics, computer science, and engineering. There are 4 commonly used system i.e. Decimal, Binary, Octal, and Hexadecimal.

Decimal Number System (Base 10)

Overview:

• The most common number system used in daily life.

• Base 10 system, which means it has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

• Each digit's position in a number has a value that is a power of 10.

Example:

• The number 345 in decimal can be expressed as:

Usage:

• Used universally in everyday arithmetic and counting.

Conversion:

Binary Number System (Base 2)

Overview:

• Used primarily in computing and digital electronics.

• Base 2 system, with only two digits: 0 and 1.

• Each digit's position in a number has a value that is a power of 2.

Example:

• The binary number 1011 can be expressed as

Usage:

• Binary code is the fundamental language of computers.

• Used in digital circuits and data representation in computers.

Conversion:

Octal Number System (Base 8)

Overview:

• Base 8 system, with eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.

• Each digit's position in a number has a value that is a power of 8.

• Group by 3 bits i.e. (2^3 = 8) in a binary number.

Example:

• The octal number 345 can be expressed as:

Usage:

• Sometimes used in computing as a more compact representation of binary-coded values.

• Historically significant in early computing systems.

Conversion:

Hexadecimal Number System (Base 16)

Overview:

• Base 16 system, with sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

• Each digit's position in a number has a value that is a power of 16.

• Group by 4 bits i.e. (2^4 = 16) in a binary number.

Example:

• The hexadecimal number 1A3 can be expressed as:

Usage:

• Widely used in computer science and programming.

• Handy for representing large binary values compactly, such as memory addresses and color codes in web design.

Conversion: