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.

Over View Introduction Background Decomposition and Synthesis Variable Partitioning Basic/ Selector Optimization Multi-Output Synthesis Experiment Results Related Work Conclusion and Future Work

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.

XOR Decomposition (early work) Spectral decomposition Linear decomposition Davio 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

FLDS Look at a linear relationship between logic functions Define functional linearity to be a decomposition of the form: f ( X ) = Σ i g i ( Y ) h i ( X-Y ) where X and Y are sets of variables (Y is the subset of X), while the summation represents an XOR gate.

FLDS Look at a linear relationship between logic functions Define functional linearity to be a decomposition of the form: f ( X ) = Σ i g i ( Y ) h i ( X-Y ) where X and Y are sets of variables (Y is the subset of X), while the summation represents an XOR gate.

FLDS Look at a linear relationship between logic functions Define functional linearity to be a decomposition of the form: f ( X ) = Σ i g i ( Y ) h i ( X-Y ) where X and Y are sets of variables (Y is the subset of X), while the summation represents an XOR gate.

FLDS Look at a linear relationship between logic functions Define functional linearity to be a decomposition of the form: f ( X ) = Σ i g i ( Y ) h i ( X-Y ) where X and Y are sets of variables (Y is the subset of X), while the summation represents an XOR gate.

Background Galois Field of characteristic 2 (GF(2)) Linear independence Vectors spaces Gaussion Elimination

Field

Galois Field of characteristic 2 (GF(2))

Linear independence

Gaussion Elimination

Decomposition and Synthesis

Variable Partitioning

Basic/ Selector Optimization

Multi-Output Synthesis

Experiment Results

Related Work

Conclusion and Future Work