Ch 3. Arithmetic for computers - (3)

3. Division

• Division = ‘adder’ (subtracter) + ‘shifter’ registers
• Positive Integer에 대해서만 고려
• Algorithm

    If (partial remainder ≥ divisor) then
        quotient bit = 1;
        remainder = remainder - divisor;
    else
        quotient bit = 0;
    shift down next dividend bit
  

• Ex)
  
  • 1000 (divisor)
  • 1001010 (dividend)
  • 1001 (quotient)
  • 10 (remainder)

Division: Implementation

• Final Version을 활용
• Dividend
  • 64bits
  • Shift Right
  • Shift Left
  • register Hi
    • Remainder 저장
    • mfhi $t0
    • 32bits
  • register Lo
    • Quotient 저장
    • mflo $t1
    • 32bits

Division of signed number

• Quotient
  • Dividend와 Divisor의 sign
    • 같으면 positive
    • 다르면 negative
• Remainder
  • Dividend와 같은 sign을 가짐
• Ex)
  • +7 / 2 = 3(Q) 1(R)
  • -7 / 2 = -3(Q) -1(R)
  • +7 / -2 = -3(Q) 1(R)
  • -7 / -2 = 3(Q) -1(R)