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VLSI Arithmetic
Lecture 9:
Multipliers
Prof. Vojin G. Oklobdzija
University of California
http://www.ece.ucdavis.edu/acsel
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Multiplication Algorithm*
*from Parhami
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Multiplication Algorithm*
*from Parhami
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11 May 20044
Multiplication Algorithm*
*from Parhami
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11 May 20045
*from Parhami
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Multiplication*
*from Parhami
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Multiplication*
*from Parhami
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*from Parhami
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*from Parhami
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Multiplier Recoding**from Parhami
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*from Parhami
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Multiplication by Constants
*from Parhami
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Multiplication by Constants
*from Parhami
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Fast Multipliers
*from Parhami
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Using Higher Radix Multiplier
*from Parhami
U i Hi h R di M lti li
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Using Higher Radix Multiplier
*from Parhami
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Higher Radix Multiplier
*from Parhami
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*from Parhami
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Booths Recoding
*from Parhami
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Booths Recoding
*from Parhami
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Booths Recoding
*from Parhami
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*from Parhami
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Multiplier Design11 May 2004 23
Multiplicand Y
Multipli
er
Encoding Selectors
-2Y -Y 0 Y 2Y
Modified Booth Recording Implementation
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Higher Radix Multipliers
*from Parhami
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Tree and Array Multipliers
*from Parhami
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Tree and Array Multipliers
*from Parhami
T M lti li
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Tree Multipliers
*from Parhami
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Tree Multipliers
*from Parhami
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Generating Partial Products
*from G. Bewick
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Generating Partial Products
*from G. Bewick
G ti P ti l P d t i B th
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Generating Partial Products using Booths
Recoding
*from G. Bewick
Generating Partial Prod cts sing Booths
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Generating Partial Products using Booths
Recoding
*from G. Bewick
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Booth Partial Product Selector Logic
*from G. Bewick
Radix-2 Booth Recoded Multiplier
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11 May 200434
Radix-2 Booth Recoded Multiplier
with Negative Partial Products
*from G. Bewick
Radix 2 Booth Recoded Multiplier
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Radix-2 Booth Recoded Multiplier
with Summed Sign Extension
*from G. Bewick
Radix-2 Booth Recoded Multiplier
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Radix-2 Booth Recoded Multiplier
with Summed Sign Extension
*from G. Bewick
Radix-2 Booth Recoded Multiplier
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Radix-2 Booth Recoded Multiplier
with Summed Sign Extension and Reduced
Logic Depth
*from G. Bewick
Complete Signed Radix 2 Booth
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Complete Signed Radix-2 Booth
Recoded Multiplier
*from G. Bewick
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Tree Multipliers
*from Parhami
Reduction using 4:2 Compressors
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Reduction using 4:2 Compressors
*from G. Bewick
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Tree Multipliers
*from Parhami
M lti li Pl t i St d d G id T l
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Multiplier Placement in a Standard Grid Topology
*from G. Bewick
Floor Plan of a Multiplier
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Floor Plan of a Multiplier
*from G. Bewick
Delay Components of a Booth Recoded
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Delay Components of a Booth Recoded
Parallel Multiplier
*from G. Bewick
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Hollywood
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THE
END