On The Design Of Low-Complexity High-Speed Arithmetic Circuits In Quantum-Dot Cellular Automata Nanotechnology

For the last four decades, the implementation of very large-scale integrated systems has largely based on complementary metal-oxide semiconductor (CMOS) technology. However, this technology has reached its physical limitations. Emerging nanoscale technologies such as quantum-dot cellular automata (QCA), single electron tunneling (SET), and tunneling phase logic (TPL) are major candidate for possible replacements of CMOS. These nanotechnologies use majority and/or minority logic and inverters as circuit primitives. In this dissertation, a comprehensive methodology for majority/minority logic networks synthesis is developed. This method is capable of processing any arbitrary multi-output Boolean function to nd its equivalent optimal majority logic network targeting to optimize either the number of gates or levels. The proposed method results in different primary equivalent majority expression networks. However, the most optimized network will be generated as a nal solution. The obtained results for 15 MCNC benchmark circuits show that when the number of majority gates is the rst optimization priority, there is an average reduction of 45.3% in the number of gates and 15.1% in the number of levels. They also show that when the rst priority is the number of levels, an average reduction of 23.5% in the number of levels and 43.1% in the number of gates is possible, compared to the majority AND/OR mapping method. These results are better compared to those obtained from the best existing methods. In this dissertation, our approach is to exploit QCA technology because of its capability to implement high-density, very high-speed switching and tremendously lowpower integrated systems and is more amenable to digital circuits design. In particular, we have developed algorithms for the QCA designs of various single- and multi-operation arithmetic arrays. Even though, majority/minority logic are the basic units in promising nanotechnologies, an XOR function can be constructed in QCA as a single device. The basic cells of the proposed arrays are developed based on the fundamental logic devices in QCA and a single-layer structure of the three-input XOR function. This process leads to QCA arithmetic circuits with better results in view of dierent aspects such as cell count, area, and latency, compared to their best counterparts. The proposed arrays can be formed in a pipeline manner to perform the arithmetic operations for any number of bits which could be quite valuable while considering the future design of large-scale QCA circuits

Integrating nano-logic into an undergraduate logic design course

The goal of this work is to motivate our students and enhance their ability to address newer logic blocks namely majority gates in the existing framework. We use a K-map based methodology to introduce a few novel nano-logic design concepts for the undergraduate logic design class. We want them to possess knowledge about a few fundamental abstracted logical behaviors of future nano-devices and their functionality which in turn would motivate them to further investigate these non-CMOS emerging devices, logics and architectures. This would augment critical thinking of the students where they apply the learnt knowledge to a novel/unfamiliar situation. We intend to augment the existing standard EE and CS courses by inserting K-map based knowledge modules on nano-logic structure for stimulating their interest without significant diversion from the course framework. Experiments with our students show that all the students were able to grasp the basic concept of majority logic synthesis and almost 63 of them had a deeper understanding of the synthesis algorithm demonstrated to them

Integrating a nanologic knowledge module Into an undergraduate logic design course

This work discusses a knowledge module in an undergraduate logic design course for electrical engineering (EE) and computer science (CS) students, that introduces them to nanocomputing concepts. This knowledge module has a twofold objective. First, the module interests students in the fundamental logical behavior and functionality of the nanodevices of the future, which will motivate them to enroll in other elective courses related to nanotechnology, offered in most EE and CS departments. Second, this module can be used to let students analyze, synthesize, and apply their existing knowledge of the Karnaugh-map-based Boolean logic reduction scheme into a revolutionary design context with majority logic. Where many efforts focus on developing new courses on nanofabrication and even nanocomputing, this work is designed to augment the existing standard EE and CS courses by inserting knowledge modules on nanologic structures so as to stimulate student interest without creating a significant diversion from the course framework

Work in progress: introduction of K-map based nano-logic synthesis as knowledge module in logic design course

This work in progress reports an effort of introducing knowledge module regarding novel nano-devices and novel logic primitives in undergraduate logic design class. Our motivation is to make our students aware of fundamental abstracted logical behaviors of future nano-devices, their functionality. This effort would also help the students use their existing knowledge of K-map based logical synthesis into constructing logic blocks for novel devices that uses majority logic as basic construct. Moreover, additional to stimulating our students' interests, we are also augmenting their learning by challenging them to use their existing knowledge to analyze, synthesize and comprehend novel nano-logic issues through the worksheets and lecture modules. Whereas many efforts are focusing on developing new courses on nanofabrication and even nano-computing, we intend to augment the existing standard EE and CS courses by inserting knowledge modules on nano-logic structure for stimulating their interest without significant diversion from the course framework

Mathematical Estimation of Logical Masking Capability of Majority/Minority Gates Used in Nanoelectronic Circuits

In nanoelectronic circuit synthesis, the majority gate and the inverter form the basic combinational logic primitives. This paper deduces the mathematical formulae to estimate the logical masking capability of majority gates, which are used extensively in nanoelectronic digital circuit synthesis. The mathematical formulae derived to evaluate the logical masking capability of majority gates holds well for minority gates, and a comparison with the logical masking capability of conventional gates such as NOT, AND/NAND, OR/NOR, and XOR/XNOR is provided. It is inferred from this research work that the logical masking capability of majority/minority gates is similar to that of XOR/XNOR gates, and with an increase of fan-in the logical masking capability of majority/minority gates also increases

Majority logic synthesis

International audienceThe majority function ⟨xyz⟩ evaluates to true, if at least two of its Boolean inputs evaluate to true. The majority function has frequently been studied as a central primitive in logic synthesis applications for many decades. Knuth refers to the majority function in the last volume of his seminal The Art of Computer Programming as "probably the most important ternary operation in the entire universe. " Majority logic sythesis has recently regained signficant interest in the design automation community due to nanoemerging technologies which operate based on the majority function. In addition , majority logic synthesis has successfully been employed in CMOS-based applications such as standard cell or FPGA mapping. This tutorial gives a broad introduction into the field of majority logic synthesis. It will review fundamental results and describe recent contributions from theory, practice, and applications

A Logic Simplification Approach for Very Large Scale Crosstalk Circuit Designs

Crosstalk computing, involving engineered interference between nanoscale metal lines, offers a fresh perspective to scaling through co-existence with CMOS. Through capacitive manipulations and innovative circuit style, not only primitive gates can be implemented, but custom logic cells such as an Adder, Subtractor can be implemented with huge gains. Our simulations show over 5x density and 2x power benefits over CMOS custom designs at 16nm [1]. This paper introduces the Crosstalk circuit style and a key method for large-scale circuit synthesis utilizing existing EDA tool flow. We propose to manipulate the CMOS synthesis flow by adding two extra steps: conversion of the gate-level netlist to Crosstalk implementation friendly netlist through logic simplification and Crosstalk gate mapping, and the inclusion of custom cell libraries for automated placement and layout. Our logic simplification approach first converts Cadence generated structured netlist to Boolean expressions and then uses the majority synthesis tool to obtain majority functions, which is further used to simplify functions for Crosstalk friendly implementations. We compare our approach of logic simplification to that of CMOS and majority logic-based approaches. Crosstalk circuits share some similarities to majority synthesis that are typically applied to Quantum Cellular Automata technology. However, our investigation shows that by closely following Crosstalk's core circuit styles, most benefits can be achieved. In the best case, our approach shows 36% density improvements over majority synthesis for MCNC benchmark

Inversion optimization in majority-inverter graphs

Many emerging nanotechnologies realize majority gates as primitive building blocks and they benefit from a majority-based synthesis. Recently, Majority-Inverter Graphs (MIGs) have been introduced to abstract these new technologies. We present optimization techniques for MIGs that aim at rewriting the complemented edges of the graph without changing its shape. We demonstrate the performance of our optimization techniques by considering three cases of emerging technology design: semi-custom digital design using Spin Wave Devices (SWDs) and Quantum-Dot Cellular Automata (QCA); and logic in-memory operation within Resistive Random Access Memories (RRAMs). Our experimental results show that SWD and QCA technologies benefit from complemented edges minimization. Area, delay, and power of SWD-based circuits are improved by 13.8%, 21.1%, and 9.2% respectively, while the number of QCA cells in QCA-based circuits can be decreased by 4.9% on average. Reductions of 14.4% and 12.4% in the number of devices and sequential steps respectively can be achieved for RRAMs when the number of nodes with exactly one complemented input is increased during MIG optimization