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:
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