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![Page 1: VLSI Arithmetic - University of California, Davis › ~vojin › CLASSES › EPFL › ... · Microsoft PowerPoint - VLSI-Arithmetic-Lect-11-Division Author: vojin Created Date: 6/1/2004](https://reader034.vdocuments.us/reader034/viewer/2022042311/5ed9ff7628db2d5ca249396c/html5/thumbnails/1.jpg)
VLSI Arithmetic
Lecture 11:Division
Prof. Vojin G. OklobdzijaUniversity of California
http://www.ece.ucdavis.edu/acsel
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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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June 1, 20043
Shift/Subtract Division Algorithms
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June 1, 20044
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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June 1, 20045
Division
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June 1, 20046
Programmed Division
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June 1, 20047
Restoring Hardware Dividers
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June 1, 20048
Restoring Hardware Dividers
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June 1, 20049
Restoring Hardware Dividers
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June 1, 200410
Restoring Division
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June 1, 200411
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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June 1, 200412
Nonrestoring Division
Why it is acceptable to store an incorrect valuein the partial-remainder register?
*from Parhami
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June 1, 200413
Non-restoring Division
*from Parhami
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June 1, 200414
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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June 1, 200415
Division
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June 1, 200416
Division
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June 1, 200417
Division
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June 1, 200418
Division
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June 1, 200419
*from Parhami
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June 1, 200420
High-Radix Division
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June 1, 200421
High-Radix Division
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June 1, 200422
High-Radix Division
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June 1, 200423
SRT Division
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June 1, 200424
SRT Division
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June 1, 200425
SRT Division
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June 1, 200426
SRT Division
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June 1, 200427
Using Carry-Save Adder
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June 1, 200428
SRT Division
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June 1, 200429
*from Parhami
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June 1, 200430
Radix-4 SRT
Division
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June 1, 200431
General High-Radix Dividers
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June 1, 200432
Combined Multiply/Divide Units
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June 1, 200433
Other Methods for Division
General High-Radix DividersDivision with prescalingArray DividersDivision by Convergence
Division by repeated multiplicationDivision by reciprocation
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Multiplier DesignJune 1, 2004 34
THEEND
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Hollywood