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VLSI Arithmetic Lecture 11: Division Prof. Vojin G. Oklobdzija University of California http://www.ece.ucdavis.edu/acsel
VLSI Arithmetic
Lecture 11:Division
Prof. Vojin G. OklobdzijaUniversity of California
http://www.ece.ucdavis.edu/acsel
June 1, 20042
DivisionPart Goals
Review shift-subtract division schemesLearn about faster dividersDiscuss speed/cost tradeoffs in dividers
Part SynopsisDivision is the hardest basic operationFortunately, it is also the least commonDivision speedup: high-radix, array, ...Combined multiplication/division hardwareDigit-recurrence vs convergence division
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Shift/Subtract Division Algorithms
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DivisionDivision is more complex than multiplication:
Need for quotient digit selection or estimationPossibility of overflow: the high-order k bits of zmust be strictly less than d; this overflow checkalso detects the divide-by-zero condition.
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Division
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June 1, 20046
Programmed Division
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June 1, 20047
Restoring Hardware Dividers
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Restoring Hardware Dividers
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Restoring Hardware Dividers
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Restoring Division
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Nonrestoring and Signed Division
The cycle time in restoring division must accommodate:• shifting the registers• allowing signals to propagate through the adder• determining and storing the next quotient digit• storing the trial difference, if required
Later events depend on earlier ones in the same cycleSuch dependencies tend to lengthen the clock cycle.
Nonrestoring division algorithm assume qk–j = 1 and perform• subtraction• store the difference as the new partial remainder
(the partial remainder can become incorrect, hence the name “nonrestoring”)
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Nonrestoring Division
Why it is acceptable to store an incorrect valuein the partial-remainder register?
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Non-restoring Division
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Nonrestoring Division Example
(0 1 1 1 0 1 0 1)two / (1 0 1 0)two(117)ten / (10)ten *from Parhami
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Division
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Division
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Division
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Division
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High-Radix Division
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High-Radix Division
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High-Radix Division
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SRT Division
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SRT Division
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SRT Division
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SRT Division
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Using Carry-Save Adder
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SRT Division
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Radix-4 SRT
Division
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General High-Radix Dividers
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Combined Multiply/Divide Units
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Other Methods for Division
General High-Radix DividersDivision with prescalingArray DividersDivision by Convergence
Division by repeated multiplicationDivision by reciprocation
Multiplier DesignJune 1, 2004 34
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