**What is a Number System?**

A number system is a method of writing numbers that is a mathematical way of representing the numbers of a given set by mathematically using numbers or symbols. A number system is defined as a writing system for denoting numbers logically using digits or symbols. The numeral system represents a useful set of numbers, reflects a number’s arithmetic and algebraic structure, and offers standard representation. All numbers can be formed using the digits 0 to 9. Anyone can generate an infinite number using these digits. For instance, 156,3907, 3456, 1298, 784859, and so on.

**Number System in Computer**

Number system in computer The most commonly used number system is the binary system, also known as the base-2 number system. The binary system uses only two digits, 0 and 1, to represent all numbers and data.

Binary numbers are used extensively in digital electronics and computing because it is easy to represent them using switches, where 0 represents “off” and 1 represents “on.” This makes it possible to store and manipulate data electronically using digital circuits.

These systems are often used for representing and manipulating large binary numbers or for expressing memory addresses in a compact and easy-to-read format. Computer programs and programming languages use number system concepts to perform arithmetic operations, store data, and communicate with hardware devices.

**Types of the Number System in Computer**

There are mainly four types of the number system in computer

**Binary Number System:**The binary number system is the most fundamental number system used in computer science. It uses only two digits, 0 and 1, to represent all numbers and data.**Decimal Number System:**The decimal number system is also used in computer science, but it is not as fundamental as the binary system. It uses ten digits, 0 through 9, to represent numbers.**Octal Number System:**The octal number system uses eight digits, 0 through 7, to represent numbers. It is commonly used in computer programming and digital electronics.**Hexadecimal Number System:**The hexadecimal number system uses 16 digits, including 0 through 9 and A through F, to represent numbers. It is often used in computer programming and digital electronics.

Each of these number systems has its advantages and disadvantages, and each is used in different applications. For example, the binary number system is used to represent and manipulate data in computer hardware, while the decimal number system is used for everyday calculations. The octal and hexadecimal systems are commonly used in computer programming and digital electronics because they are more compact and easier to read than binary.

**Frequently Asked Questions**

Here are the FAQs on the number system in computer

**Q1: Why is the binary number system used in computers?****Ans:** Computers use binary number system because it is the simplest number system to implement using electronic components. Binary system can represent all data and instructions in a computer as a combination of 0 and 1, which can be easily represented using electronic switches.

**Q2: How are numbers converted between binary, decimal and hexadecimal systems?****Ans:** To convert a binary number to a decimal number, you can use the method of multiplying each digit by the power of 2, starting from the rightmost digit, and adding up the results. To convert a decimal number to a binary number, you can use the method of dividing the decimal number by 2 and noting the remainder at each step. To convert between hexadecimal and binary, you can first convert the hexadecimal number to its equivalent binary number, and vice versa.

**Q3: What is the significance of different number systems in computer programming?****Ans:** Different number systems are used in computer programming to represent and manipulate data in different ways. For example, the hexadecimal number system is often used in computer programming because it represents a more compact way of representing binary data. The choice of number system depends on the specific application and requirements of the computer system.

**Q4: What is the purpose of using different number systems in computers?****Ans:** Different number systems are used in computers to represent and manipulate data in different ways. For example, the binary number system is used to represent data in a computer’s memory and in communication between computer devices, while the hexadecimal number system is often used in computer programming. The choice of number system depends on the specific application and requirements of the computer system.

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