Number Systems and Conversions

Number Systems

Types of Number Systems

• Decimal Number System:
  • Base 10
  • Uses digits 0-9
  • Most widely used number system
• Binary Number System:
  • Base 2
  • Uses digits 0-1
  • Used in computer systems
• Octal Number System:
  • Base 8
  • Uses digits 0-7
  • Used in computer systems
• Hexadecimal Number System:
  • Base 16
  • Uses digits 0-9 and A-F
  • Used in computer systems and programming

Number System Conversions

• Binary to Decimal:
  • Each binary digit (bit) is multiplied by 2^x, where x is the position of the bit (starting from 0)
  • The results are added together to get the decimal equivalent
• Decimal to Binary:
  • Divide the decimal number by 2 and keep track of the remainders
  • The remainders, in reverse order, form the binary equivalent
• Hexadecimal to Decimal:
  • Convert each hexadecimal digit to its decimal equivalent (A=10, B=11, ..., F=15)
  • Combine the decimal equivalents to get the final decimal number

Number System Operations

• Addition:
  • Same as decimal addition, but using the base of the number system
• Subtraction:
  • Same as decimal subtraction, but using the base of the number system
• Multiplication:
  • Same as decimal multiplication, but using the base of the number system
• Division:
  • Same as decimal division, but using the base of the number system

Understand different number systems, including decimal, binary, octal, and hexadecimal, and learn how to convert between them. Practice number system operations like addition, subtraction, multiplication, and division.