Ch 3. Arithmetic for computers - (2)

2. Multiplication

• Multiplying = ‘add’ + ‘shift’ operation
  • with binary numbers
• Positive integer에 대해서만 고려
• Ex)
  
  • 0010 (multiplicand)
  • 1001 (multiplier)
  • 0010010 (product)

Multiplication: Implementation

• Version 1
  
  • Multiplicand: Shift Left
  • Product: doesn’t move
  • Multiplicand: 64bits
  • Multiplier: 32bits
  • Product: 64bits
  • 64-bit ALU
• Version 2
  
  • Multiplicand: doesn’t move
  • Product: Shift Right
  • Multiplicand: 32bits
  • Multiplier: 32bits
  • Product: 64bits
  • 32-bit ALU
• Version 1 → Version2: Save Spaces & Hardware reducing
• Final Version
  
  • Multiplier -> Product register

  

Multiplication of negative numbers

1. Negate negative number(s)
   • -3 => 3
2. unsigned multiplication 수행
   • 3 * 4 = 12
3. negate the result
   • 12 => -12

• Another way: Booth algorithm