1. 1 Stochastic Logic Beyond CMOS... Prof. Mingjie Lin

2. 2 Computing Beyond CMOS Intense research into novel materials and devices: Carbon Nanotubes… Molecular Switches… Biological Processes…

3. 3 Computing Beyond CMOS Many technologies still in exploratory phase: ! 

4. 4 Nanoscale Circuits Topological constraints. Inherent randomness. High defect rates. Features: Challenges: High density of bits. Identify general traits that impinge upon logic synthesis: carbon nanowire crossbar

5. 5 Circuit Modeling logic 0 1 0 0 1 Characterize probability of outcomes. inputsoutputs Model defects, variations, uncertainty, etc.:

6. 6 Circuit Modeling logic Functional description is Boolean: inputsoutputs

7. 7 Consider a probabilistic interpretation: logic stochastic logic inputsoutputs Circuit Modeling

8. 8 stochastic logic Stochastic Logic inputsoutputs 0 1 0 0,1,1,0,1,0,1,1,0,1,… 1,0,0,0,1,0,0,0,0,0,… p 1 = Prob(one) p 2 = Prob(one) serial bit streams Consider a probabilistic interpretation:

9. 9 stochastic logic Stochastic Logic inputsoutputs 0 1 0 Consider a probabilistic interpretation:

10. 10 stochastic logic Stochastic Logic 0 1 0 0 1 0 0 1 0 1 0 0 0 p 1 = Prob(one) p 2 = Prob(one) parallel bit streams Consider a probabilistic interpretation:

11. 11 stochastic logic Stochastic Logic 0 1 0 parallel bit streams Consider a probabilistic interpretation:

12. 12 stochastic logic Stochastic Logic Interpret outputs according to fractional weighting: 0 1 0

13. 13 Synthesis of Stochastic Logic Circuit that computes a probability distribution corresponding to a logical specification. Given a technology characterized by: Synthesize: High degree of structural parallelism. Inherent randomness in logic/interconnects. Cast problem in terms of arithmetic operations. Perform synthesis with binary moment diagrams. Strategy:

14. 14 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. Probabilistic Bundles 0 1 0 0 1 x X

15. 15 Arithmetic Operations Multiplication(Scaled) Addition ba BPAP CPc    )()( )( ) )1( ()](1[)()( )( bsas BPSPAPSP CPc   

16. 16 Nanowire Crossbar (idealized)

17. 17 Nanowire Crossbar (idealized) Randomized connections, yet nearly one-to-one.

18. 18 Shuffled AND

19. 19 Takes the AND of randomly chosen pairs. Multiplication Shuffled AND

20. 20 Bundleplexing

21. 21 Scaled Addition Randomly selection of wires from different bundles,. Randomly selection of wires from different bundles, according to a fixed ratio. ¾ Bundleplexer

22. 22 Stochastic Logic Shuffled ANDs, Bundleplexers { { A 0 A 1... { A n } B

23. 23 Stochastic Logic Shuffled ANDs, Bundleplexers { { { }... 1 0 1

24. 24 Lecture schedule See Webpage: www.eecs.ucf.edu/~mingjie/EEL4783

25. 25 Final issues Come by my office hours (right after class) Any questions or concerns?