CBSE 10th Class Unit 1 - Number System

 Number System

A number system is a system for representing numbers. Different number systems use different bases (or radices) to represent numbers.

Common Number Systems:

1. Decimal Number System (Base-10):
• Uses 10 digits (0-9) to represent numbers.
• Each digit's position represents a power of 10.
• Example: 123 = 1 * 10^2 + 2 * 10^1 + 3 * 10^0
2. Binary Number System (Base-2):
• Uses 2 digits (0 and 1) to represent numbers.
• Each digit's position represents a power of 2.
• Example: 101 = 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 5
3. Octal Number System (Base-8):
• Uses 8 digits (0-7) to represent numbers.
• Each digit's position represents a power of 8.
• Example: 25 = 2 * 8^1 + 5 * 8^0 = 21
4. Hexadecimal Number System (Base-16):
• Uses 16 digits (0-9 and A-F) to represent numbers.
• Each digit's position represents a power of 16.
• Example: 2F = 2 * 16^1 + 15 * 16^0 = 47

Number System Conversion

Converting between number systems involves changing the base of the number. Here are some common conversion methods:

• Decimal to Binary: Repeated division by 2, remainders form the binary number.
• Binary to Decimal: Sum of each digit multiplied by its corresponding power of 2.
• Decimal to Octal: Repeated division by 8, remainders form the octal number.
• Octal to Decimal: Sum of each digit multiplied by its corresponding power of 8.
• Decimal to Hexadecimal: Repeated division by 16, remainders form the hexadecimal number.

Hexadecimal to Decimal: Sum of each digit multiplied by its corresponding power of 16.