# Number Systems

The language we use to communicate with each other is comprised of words and characters. We understand numbers, characters and words. But this type of data is not suitable for computers. Computers only understand the numbers.

So, when we enter data, the data is converted into electronic pulse. Each pulse is identified as code and the code is converted into numeric format by ASCII. It gives each number, character and symbol a numeric value (number) that a computer understands. So to understand the language of computers, one must be familiar with the number systems.

The Number Systems used in computers are:

• Binary number system
• Octal number system
• Decimal number system

## Binary number system

It has only two digits '0' and '1' so its base is 2. Accordingly, In this number system, there are only two types of electronic pulses; absence of electronic pulse which represents '0'and presence of electronic pulse which represents '1'. Each digit is called a bit. A group of four bits (1101) is called a nibble and group of eight bits (11001010) is called a byte. The position of each digit in a binary number represents a specific power of the base (2) of the number system.

## Octal number system

It has eight digits (0, 1, 2, 3, 4, 5, 6, 7) so its base is 8. Each digit in an octal number represents a specific power of its base (8). As there are only eight digits, three bits (23=8) of binary number system can convert any octal number into binary number. This number system is also used to shorten long binary numbers. The three binary digits can be represented with a single octal digit.

## Decimal number system

This number system has ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) so its base is 10. In this number system, the maximum value of a digit is 9 and the minimum value of a digit is 0. The position of each digit in decimal number represents a specific power of the base (10) of the number system. This number system is widely used in our day to day life. It can represent any numeric value.

This number system has 16 digits that ranges from 0 to 9 and A to F. So, its base is 16. The A to F alphabets represent 10 to 15 decimal numbers. The position of each digit in a hexadecimal number represents a specific power of base (16) of the number system. As there are only sixteen digits, four bits (24=16) of binary number system can convert any hexadecimal number into binary number. It is also known as alphanumeric number system as it uses both numeric digits and alphabets.

## Importance of Number Systems in Computer Science

Understanding particular range structures is important in computer technology for several reasons:

• Memory Management: Computers use binary systems for memory management. Knowing a way to convert between binary, octal, decimal, and hexadecimal permits successfully dealing with memory and storage.
• Programming: In programming, hexadecimal is regularly used to represent memory addresses and binary-coded values. Octal and binary representations are crucial for bitwise operations.
• Data Transmission: Binary is important for record transmission in computer structures. When records are transmitted or saved, their miles are frequently transformed to binary for efficient processing.
• Debugging: Hexadecimal is normally utilized in debugging, and it is a low-level programming language. Memory dumps and machine code are frequently provided in hexadecimal format.
• Digital Electronics: Understanding binary is essential in digital electronics, wherein circuits are characteristically based on binary signals.
• Representation of Colors: In graphics and web development, hexadecimal is frequently used to represent colorations. Each coloration element (RGB) is represented with a resource of hexadecimal digits.
• Encryption and Hashing: Many encryption algorithms and hash tables carry out binary information, making binary models required in cybersecurity.

1) Binary System

• Advantages: Direct correspondence with digital logic and electronic devices.
• Disadvantages: Lengthy illustration for massive numbers, limited expressiveness for decimal fractions.

2) Octal System

3) Decimal System

• Advantages: Easily understable, modern for vast arithmetic.

• Advantages: Compact representation of binary, widely utilized in programming.

5) Contextual Considerations

• Efficiency in Storage: Binary and hexadecimal are more simple. Decimal may additionally require greater space.
• Ease of Human Comprehension: Decimal is most intuitive, even as binary and hexadecimal may be tough.
• Programming and Debugging: Hexadecimal is preferred; binary and octal may be used in unique instances.
• Digital Electronics: Binary is natural; decimal is hardly ever used.
• Mathematical Operations: Decimal is better; others might also require extra conversion steps.

In precis, the selection of the number system is based on application necessities, ease of comprehension, and performance in storage and processing. Each type has its strengths and weaknesses, serving precise purposes in computer technology.

## Conclusion

In the large panorama of computer technological knowledge, number systems function as the foundation for all computations, facts, and illustrations. From the binary language of machines to the more user-friendly decimal system and the convenient octal and hexadecimal, these systems facilitate communication among human beings and computer systems.

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