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Division

Division. Perform binary division of two numbers. Define dividend, divisor, quotient, and remainder. Explain how division is accomplished in computer hardware. Construct a simple program which uses MIPS integer multiplication and division . Definitions (Pg 237). Dividend

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Division

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  1. Division Perform binary division of two numbers. Define dividend, divisor, quotient, and remainder. Explain how division is accomplished in computer hardware. Construct a simple program which uses MIPS integer multiplication and division

  2. Definitions (Pg 237) • Dividend • The first operand of a divide operation • Divisor • The second operand of a divide operation • Quotient • The primary result of a divide operation • Remainder • The secondary result ofa division operation 14 / 5 = 2rem4 CS2710 Computer Organization

  3. Division (Long Approach) • Solve the following CS2710 Computer Organization

  4. Division Algorithm • Check for 0 divisor first! • Long division approach • If divisor ≤ dividend bits • 1 bit in quotient, subtract • Otherwise • 0 bit in quotient, bring down next dividend bit • Restoring division • Do the subtract, and if remainder goes < 0, add divisor back • Signed division • Divide using absolute values • Adjust sign of quotient and remainder as required CS2710 Computer Organization

  5. Faster Division • Can’t use parallel hardware as in multiplier • In multiplication, we can compute partial products simultaneously • In division, we have to compute differences at each step • Faster dividers (e.g. SRT division) generate multiple quotient bits per step • Still require multiple steps, using guesses and corrections • Uses a lookup table that must be precomputed • Source of infamous 1994 Pentium flaw

  6. MIPS Division • Use HI/LO registers for result • HI: 32-bit remainder • LO: 32-bit quotient • Instructions • div rs, rt / divurs, rt • No overflow or divide-by-0 checking! • Software must perform checks if required • Use mfhi, mflo to access result • $hi and $lo are left unchanged during divide-by-0! • They contain whatever values they had prior to divide-by-0 Chapter 3 — Arithmetic for Computers — 6

  7. In Class Example • Write an assembly program which will perform the following: • Read two integer numbers from the user • Print out their product • Print out their quotient • Print out the remainder (If the numbers are not evenly divisible) CS2710 Computer Organization

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