CLASS 9TH MATH || NUMBER SYSTEM || REVISION CLASS || LEC - 1

Number System
A number system is a method of representing numbers using digits or symbols in a consistent manner. It defines the rules for writing and interpreting numerical values. The most common number system we use is the decimal system, which has a base of 10 and uses digits from 0 to 9.
Key Components of a Number System:
Base (or Radix): The number of unique digits available in the system. For example, the decimal system has a base of 10.
Digits: The symbols used to represent numbers. In the decimal system, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Common Number Systems:
Decimal System (Base-10): The everyday number system we use.
Binary System (Base-2): Uses only two digits: 0 and 1. Widely used in computers.
Octal System (Base-8): Uses digits from 0 to 7.
Hexadecimal System (Base-16): Uses digits from 0 to 9 and letters A to F.
Number System Conversion:
Numbers can be converted between different number systems. This involves understanding the place value of each digit and applying appropriate algorithms.
Example:
Decimal to Binary:
Divide the decimal number repeatedly by 2.
Record the remainders in reverse order.
Binary to Decimal:
Multiply each binary digit by its corresponding power of 2.
Sum up the results.
Applications of Number Systems:
Computer Science: Binary, octal, and hexadecimal systems are fundamental in computer architecture and programming.
Digital Electronics: Binary system is used to represent digital signals.
Cryptography: Different number systems are used in encryption and decryption algorithms.