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What is a Number System?
It includes a set of symbols as well as rules for using those symbols in order to conduct arithmetic operations such as addition, subtraction, multiplication, and division. The decimal system, often known as the base-10 system, is the most commonly used number system by humans, with ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The value of each digit in the decimal system is determined by its position or place value within a number. The one’s place is represented by the rightmost digit, the tens place by the next digit to the left, the hundreds place by the following digit, and so on. In the number 352, for example, digit 2 is in the one’s place, the digit 5 is in the tens place, and the digit 3 is in the hundreds place.
Decimal numbers are based on powers of 10. The value of each digit is calculated by multiplying the digit by the matching power of ten. In the number 352, for example, the digit 2 in the one’s place has a value of 2 0 = 2 1 = 2, the digit 5 in the tens place has a value of 5 10 = 50, and the digit 3 in the hundreds place has a value of 3 102 = 3 100 = 300.
Other number systems, in addition to the decimal system, have been used in various situations. In our article Number System PDF in Hindi, Here are a few examples:
1. Binary system(base-2): This system relies on just two digits, 0 and 1. It’s quite frequent in computer systems and digital electronics. Each digit in binary represents a power of two, with the rightmost digit representing 00, the next digit to the left representing 01, the following digit having 02, and so on.
2. Octal system (base-8): This system employs eight numbers ranging from 0 to 7. Octal is used in computers and programming on occasion, primarily to represent sets of three binary digits. The value of each number indicates a power of eight.
3. Hexadecimal system (base-16): This system utilizes sixteen digits, ranging from 0 to 9 and A to F, with A representing 10, B representing 11, and so on up to F representing 15. In software development and digital systems, hexadecimal is extensively utilized. The value of each number indicates a power of sixteen.
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Uses Of Number System PDF in Hindi
The Following applications and uses of Number System PDF in Hindi are given below:
1. Algebra and Mathematics: The foundation of arithmetic and mathematical operations is number systems. They enable us to do addition, subtraction, multiplication, and division computations. The decimal system is most useful for daily calculations, whereas the binary, octal, and hexadecimal systems are utilized in computer science and digital electronics.
2. Computer Science and Programming: In computer science and programming, binary, octal, and hexadecimal number systems are widely employed. Computers use a binary system of ones and zeros to store and process information. Octal and hexadecimal systems are employed in programming languages to define memory locations, bitwise operations, and data processing because they are more compact representations of binary data.
3. Digital Electronics: In digital electronics, where electrical circuits and systems are built to analyze and modify information stored in digital number systems are critical. Binary number systems are used to represent and handle digital data, allowing advanced technologies such as microprocessors, memory units, and digital communication networks to be developed.
4. Cryptography: In cryptographic methods and encryption techniques, number systems play an important role. In the encryption and decryption tasks, many number systems, such as modular arithmetic and finite fields, are employed. These systems lay the mathematical research for secure communication and data security.
5. Measurement Systems: In systems of measurement, number systems are used to represent and quantify physical quantities. The decimal system, for example, is employed in the metric system, where length, weight, and time units are expressed and converted using powers of 10. Other measuring methods, such as binary-coded decimals (BCD), are used in particular applications such as expressing and manipulating decimal values in electronic systems.
6. Number Representation and Encoding: Various number systems are used to represent and encode data in a variety of ways. In barcodes, for example, the Universal Product Code (UPC) system employs decimal digits to indicate product information, but the QR code system uses a two-dimensional pattern of numeric, alphabetic, and binary data.
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