VLSI Arithmetic Lect 9 Multiplier

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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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    Multiplication Algorithm*

    *from Parhami

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    *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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    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


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