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ECE 667
ECE 667
Spring 2009
Spring 2009
Synthesis and Verification
of Digital Systems
Multi-level Logic Minimization
Multi-level Logic Minimization
Factored Forms
Factored Forms
Slides adopted (with permission) from A. Kuehlmann, UC Berkeley 2003
Slides adopted (with permission) from A. Kuehlmann, UC Berkeley 2003

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Outline
Outline
•
Factored forms
–
Motivation: multi-level logic representation
–
Definitions, theory, examples
•
Manipulation of Boolean networks
–
Algebraic (structural) vs Boolean methods
•
Decomposition
•
Extraction
•
Factorization
•
Substitution (elimination)
•
Collapsing

3
General Logic Structure
General Logic Structure
•
Combinational optimization (CL blocks)
–
Keep latches/registers at current positions, keep their function
–
Optimize combinational logic domains expressed as multi-level logic
– Need efficient representation of multi-level logic

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Multi-level Logic
Multi-level Logic
•
Logic represented as a network of logic gates from cell library
•
Multi-level logic optimization
–
Logic decomposition and optimization
–
Technology mapping

5
Optimization Criteria for Synthesis
Optimization Criteria for Synthesis
The optimization criteria for multi-level logic is to
minimize
some function of:
1.
Area occupied by the logic gates and interconnect
(approximated
by
literals = transistors
in technology independent optimization)
2.
Critical path delay
of the longest path through the logic
3.
Degree of testability
of the circuit, measured in terms of the
percentage
of faults covered by a specified set of test vectors for
an approximate fault model (e.g. single
or multiple stuck-at
faults)
4.
Power
consumed by the logic gates
5.
Noise Immunity
6.
Physical design constraints

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Transformation-based Synthesis
Transformation-based Synthesis
•
All modern synthesis systems are build that way
– set of transformations that change network representation
•
work on uniform network representation
–
“script” or “scenario” that can combine those transformations to a
overall greedy
•
Transformations differ in:
– the scope they are applied
• local scope versus global restructuring
– the domain they optimize
•
combinational versus sequential
•
timing versus area
• technology independent versus technology dependent
– the underlying algorithms they use
• BDD based, SAT based, structure based

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Global vs Local Transformations
Global vs Local Transformations
•
Global transformations restructure the entire network
–
merging nodes
–
spitting nodes
–
removing/changing connections between nodes, etc.
•
Local transformations optimize the function of one node of the

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