What is a number system in computer?
A Number System is a way of representing numbers using a set of symbols and rules. It helps in performing arithmetic operations and organizing numerical data. Different number systems are used in various fields, including mathematics, computing, and daily life.
Types of Number Systems:
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
1. Decimal Number System
The Decimal Number System is the most commonly used numbering system worldwide, both in everyday life and in complex scientific calculations. It is a base-10 system, meaning it utilizes ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is represent as 34510 or (333)10
Daily Life: Used in currency, measurements, and general arithmetic. Science and Engineering: Crucial for precision in measurements and calculations. Computing: While computers primarily use binary, decimal is often used in high-level processing.
2. Binary Number System
The binary number system is the foundation of modern computing. It uses only two digits 0 and 1 to represent all numerical values. This system is essential because computers operate using electrical signals that have two states: ON (1) and OFF (0). It is represent as 101112 or (1010101)2
Each binary digit (or "bit") corresponds to a power of 2, which makes binary efficient for processing and storing data. For example, the decimal number 5 is represented in binary as 101.
Binary is used in computer memory, digital circuits, and data encoding. It's also the basis for more complex numbering systems, like octal (base-8) and hexadecimal (base-16), which are useful for programming and hardware design.
3. Octal Number System
The octal number system is a base-8 system, meaning it uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. It is represent as 458 or (77)8. It's commonly used in computing, especially for representing binary numbers more compactly, since each octal digit corresponds to three binary digits.
It was more commonly used in early computing systems but has mostly been replaced by hexadecimal for readability and efficiency.
4. Hexadecimal Number System
The Hexadecimal Number System is a base-16 numbering system that uses 16 distinct symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F The letters A to F represent values from 10 to 15 in decimal. (A=10, B=11, C=12, D=13, E=14, F=15). It is represent as AFB16 or (7FD)16.
Commonly used in computer memory addressing, digital color representation, and machine-level programming.
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