# University of Twente Student Theses

## The theory and practice of probabilistic CMOS

Oudshoorn, Luuk
(2016)
*The theory and practice of probabilistic CMOS.*

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Abstract: | It is expected that in the future noise will become dominant in minimum size CMOS logic, inducing probabilistic behaviour. This allows for a trade off between performance and energy consumption. The trade off can be visualized with an Energy-Probability (E-P) curve, which defines the relationship between energy consumption and probability of correctness. This work presents a more realistic view on probabilistic CMOS behaviour for both isolated logic gates and connected systems. Theoretically, the probability of correctness of an ideal CMOS system in the presence of noise can be represented by a function of the energy consumed, the so called error function. However, CMOS speed drops rapidly around the threshold voltage. This introduces additional errors when signals miss the setup time deadline at their next sample point. The exact probability at a specific supply voltage level is influenced by factors such as noise levels, operating frequency, transistor size and temperature. Current models of Probabilistic CMOS ignore these imperfections and are therefore unrealistic at low supply voltage levels. At a system level, designs can be made with Probabilistic CMOS. Similar to conventional deterministic logic, such designs should ideally be made up of separately characterized standard building blocks. Current models of probabilistic systems only model the propagation of noise and errors through a system. In order to get a better model of probabilistic systems, errors due to missed deadlines should be added to the models of probabilistic systems. A missed deadline in this context is a changing signal that does not assume the correct value before the next sample moment. In contrast to conventional digital logic, these propagation delays have a large variance. When a more accurate prediction of the expected total error of a probabilistic system can be made for a specific energy distribution, an algorithm can be developed that finds the optimal energy distribution for a certain total error. For a system with two independent parts an algorithm was developed that can find the optimal energy distribution for low expected errors. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 53 electrotechnology |

Programme: | Electrical Engineering MSc (60353) |

Link to this item: | https://purl.utwente.nl/essays/69625 |

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