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Computing Beyond CMOS

Computing Beyond CMOS. Intense research into novel materials and devices:. Carbon Nanotubes…. Biological Processes…. Molecular Switches…. c. Computing Beyond CMOS. Many technologies still in exploratory phase:. !. Nanoscale Circuits.

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Computing Beyond CMOS

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  1. Computing Beyond CMOS Intense research into novel materials and devices: Carbon Nanotubes… Biological Processes… Molecular Switches… IWLS 2007

  2. c Computing Beyond CMOS Many technologies still in exploratory phase: ! IWLS 2007

  3. Nanoscale Circuits Identify general traits that impinge upon logic synthesis: • Topological constraints. • Inherent randomness. • High defect rates. Features: • High density of bits. Challenges: carbon nanowire crossbar IWLS 2007

  4. Synthesis of Stochastic Logic Given a technology characterized by: • Circuit that computes a probability distribution corresponding to a logical specification. • High degree of structural parallelism. • Inherent randomness in logic/interconnects. Synthesize: Strategy: • Cast problem in terms of arithmetic operations. • Perform synthesis with binary moment diagrams. IWLS 2007

  5. Probabilistic Bundles 0 1 x 0 X 0 1 A real value x in [0, 1] is encoded as a stream of bits X.For each bit, the probability that it is one is: P(X=1) = x. IWLS 2007

  6. = c P ( C ) = c P ( C ) = P ( A ) P ( B ) = + - P ( S ) P ( A ) [ 1 P ( S )] P ( B ) = a b = + - s a ( 1 s ) b Arithmetic Operations Multiplication (Scaled) Addition IWLS 2007

  7. Synthesis Strategy • From circuit, construct a data structure called a multiplicative binary moment diagram (*BMD). • Manipulate the *BMD into the right form. • Implement a stochastic circuit with Shuffled AND gates and Bundleplexors. IWLS 2007

  8. f x x x x x x x x 2 x x x x = + + - 1 2 3 1 2 4 3 4 1 2 3 4 Arithmetic Functions IWLS 2007

  9. f w f w f x = + L L R R f x x x x x x x x 2 x x x x = + + - 1 2 3 1 2 4 3 4 1 2 3 4 f f L R Construct *BMD See R. Bryant, “Verification of Arithmetic Circuits with BMDs,” 1995. IWLS 2007

  10. f x x x x x x x x 2 x x x x = + + - 1 2 3 1 2 4 3 4 1 2 3 4 Split *BMD positive negative

  11. X f x x x x x x x x = + + 1 2 3 1 2 4 3 4 P f x x x x x x x x 2 x x x x = + + - 1 2 3 1 2 4 3 4 1 2 3 4 Normalize positive

  12. w w x x X BUX SAND X f f f f L L R R Implement Stochastic Logic IWLS 2007

  13. Implement Stochastic Logic IWLS 2007

  14. Size of Stochastic Circuits

  15. Error Percentages

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