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