Lecture 4

• Octal Number System


  Number system with base value 8, uses digits 0-7
• Converting Octal to Decimal

  1. Multiply each digit with place value

  2. Add results

  
• Octal numbers are useful for representation of UTF8 numbers
• Converting Decimal to Octal

  1. Divide decimal by 8

  2. Remainder becomes least significant digit

  3. Quotient becomes next dividend

  4. Repeat

  
• Octal-Decimal Conversion

  Changing representation of a number from one base to another

  
• Octal Numbers


  • Use digits 0 to 7
  • Have a base of 8
• Converting Octal to Decimal (Steps)

  1. Multiply each digit with place value

  2. Add results

  
• Converting Binary to Octal

  1. Divide binary into groups of 3 digits

  2. Convert groups to equivalent octal digits

  
• Hexadecimal Number System


  Number system with base value 16, uses digits 0-9 and A-F

  
• Hexadecimal numbers are useful for handling memory address locations
• Decimal to Hexadecimal Conversion


  • Divide decimal by 16
  • Remainder becomes least significant digit
  • Quotient becomes next dividend
  • Repeat

  
• Converting Binary to Hexadecimal

  1. Divide binary into groups of 4 digits

  2. Convert groups to equivalent hex digits

  
• Binary Addition


  Carry over occurs when result equals 2
• Binary Subtraction


  1. Borrow 1 when subtracting 1 from 0

  2. Reduce 1 in borrowing column by 1
• 1's Complement


  Toggle all bits, 0 to 1 and 1 to 0
• 2's Complement


  1 added to 1's complement
• In 2's complement, MSB represents sign, 0 for positive, 1 for negative
• Finding 2's Complement


  Start from LSB, find first 1, then flip all bits to the left of that 1
• If all bits are 1 in 1's complement, add 1 to get 2's complement
• Minus numbers are represented in 2's complement