let7-Division I

# Computer Arithmetic: Algorithms and Hardware Designs

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CSE 246: Computer Arithmetic Algorithms and Hardware Design Instructor: Prof. Chung-Kuan Cheng Fall 2006 Lecture 7 Division

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CSE 246 2 Topics: Division Restoring Division Nonrestoring Division High Radix Division
CSE 246 3 Division – Iteration effort Pencil and paper method: ( A=Q × B+2 -n R and R<B ) 1 bit partial quotient per iteration, n iterations A =0.111 0, B =0.010; Q = A / B. Q i : Partial Quotient R i : Partial Remainder R i+1 = R i – B × Q i Q = 0.1110 + 1 0 0 1 1 0 1 0 R 0 = A 1 0 1 0 1 1 0 R 2 1 0 1 0 1 0 0 R 3 0 0 0 1 0 0 R 4 1 0 1 0 1 1 0 0.1 1 0 0 0 R 1 Q 1 = 0.1 Q 2 = 0.01 Q 3 = 0.001 Q 4 = 0.0000

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CSE 246 4 Division – Memory effort Lookup table is the simplest way to obtain multiple partial quotient bits in each iteration. SRT method: a lookup tables stores m -bit partial quotients decided by m bits of partial remainder and m bits of divisor. Table size: 2 2m × m STR method is limited by memory wall.
CSE 246 5 Division – Solution space Iteration Effort Memory Effort Arithmetic Effort Memory Wall Pencil-and-paper SRT Prescaling Taylor Expansion Low area Series Expansion Low latency Our target

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