Abstract To present a novel logic synthesis method to reduce the area of XOR-based logic functions....
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![Page 1: Abstract To present a novel logic synthesis method to reduce the area of XOR-based logic functions. Idea: To exploit linear dependency between logic sub-](https://reader035.fdocuments.in/reader035/viewer/2022062305/5697bf821a28abf838c85dac/html5/thumbnails/1.jpg)
Functionally Linear Decomposition and Synthesis of Logic Circuits for FPGA
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Abstract
To present a novel logic synthesis method to reduce the area of XOR-based logic functions.
Idea: To exploit linear dependency between
logic sub- functions to create an implementation based on an XOR relationship with a lower area overhead.
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Over ViewIntroductionBackgroundDecomposition and SynthesisVariable PartitioningBasic/ Selector OptimizationMulti-Output SynthesisExperiment ResultsRelated WorkConclusion and Future Work
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Introduction
The XOR-based logic functions are an important type of functions, heavily used in arithmetic, error correcting and telecommunication circuits.
Focus on XOR-based logic functions and show that they exhibit a property that can be exploited for area reduction in this work.
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XOR Decomposition (early work)
Spectral decompositionLinear decompositionDavio expansion + help of BDDs (Reed-Muller logic equation) Look for x-dominators in a BDD that indicate
a presennce of an XOR gate Tabular methods based on AC decomposition
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FLDS
Look at a linear relationship between logic functions
Define functional linearity to be a decomposition of the form:
f( X ) = Σi g i ( Y ) hi ( X-Y ) where X and Y are sets of variables (Y is the
subset of X), while the summation represents an XOR gate.
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FLDS
Look at a linear relationship between logic functions
Define functional linearity to be a decomposition of the form:
f( X ) = Σi g i ( Y ) hi ( X-Y ) where X and Y are sets of variables (Y is the
subset of X), while the summation represents an XOR gate.
f is the weighted sum of gi
weighting factors
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FLDS
Look at a linear relationship between logic functions
Define functional linearity to be a decomposition of the form:
f( X ) = Σi g i ( Y ) hi ( X-Y ) where X and Y are sets of variables (Y is the
subset of X), while the summation represents an XOR gate.
f is the weighted sum of gi
weighting factors
Can synthesize XOR logic functions by
Davio and Shannon’s expansions
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FLDS
Look at a linear relationship between logic functions
Define functional linearity to be a decomposition of the form:
f( X ) = Σi g i ( Y ) hi ( X-Y ) where X and Y are sets of variables (Y is the
subset of X), while the summation represents an XOR gate.
basis vectors
selector vectors
XOR gates
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Background
Galois Field of characteristic 2 (GF(2))Linear independenceVectors spacesGaussion Elimination
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Field
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Galois Field of characteristic 2 (GF(2))
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Linear independence
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Gaussion Elimination
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Decomposition and Synthesis
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Variable Partitioning
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Basic/ Selector Optimization
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Multi-Output Synthesis
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Experiment Results
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Related Work
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Conclusion and Future Work