Logic Synthesis n -Basic Concepts and Tools n Tao Lin n Ohio Universtiy n February 17, 1998.

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Presentation transcript:

Logic Synthesis n -Basic Concepts and Tools n Tao Lin n Ohio Universtiy n February 17, 1998

n Introductory to some basic concepts; n Espresso; n Brief description to the BDD (Binary Decision Diagram).

F oundation for: n combinational and sequential synthesis n testing n timing and false paths n formal verication n asynchronous synthesis n automata theory n optimal clocking schemes n hazard analysis n power estimation n general combinatorics.

if f 1 = B n, f is the tautology, i.e. f  1; if f 0 = B n, (f 1 =  ) f is not satisfiable; if f(x) = g(x) for all x  B n, then f and g are equivalent; x 1 ; x 2 ; … are variables; x 1 ; x 1 ; x 2 ; x 2 ; … are literals;

A cover is prime irredundant if all its cubes are prime (irredundant). A prime of f is essential (essential prime) if there is a min-term (essential vertex) in that prime but in no other prime.

Shannon (Boole) Cofactors

Binary Recursion Tree

Unate Functions and Unate Covers A function is unate in x i if it is either positive unate or negative unate in x i.

Unate covers F have many extraordinary properties:  If a cover F is minimal with respect to singlecube containment, all of its cubes are essential primes.  In this case F is the unique minimum cube representation of its logic function.  A unate cover represents the tautology iff it contains a cube with no literals, i.e. a single tautologous cube.

IRREDUNDANT

EXPAND

Main idea of EXPAND

REDUCE

Reduce is order dependent.

REDUCE Algorithm

Unate Algorithm for SCCC

LSTGASP

A Brief Description of BDD (Binary Decision Diagram)

Acknowledgement n Most of the materials used here were selected from EE219b course note of UC- Berkeley. The author of these notes is Mr. R.K.Brayton. n Many thanks to people who give me help on preparing this talk.