An Optimal Gate Design for the Synthesis of Ternary Logic Circuits

Department of Electrical EngineeringOver the last few decades, CMOS-based digital circuits have been steadily developed. However, because of the power density limits, device scaling may soon come to an end, and new approaches for circuit designs are required. Multi-valued logic (MVL) is one of the new approaches, which increases the radix for computation to lower the complexity of the circuit. For the MVL implementation, ternary logic circuit designs have been proposed previously, though they could not show advantages over binary logic, because of unoptimized synthesis techniques. In this thesis, we propose a methodology to design ternary gates by modeling pull-up and pull-down operations of the gates. Our proposed methodology makes it possible to synthesize ternary gates with a minimum number of transistors. From HSPICE simulation results, our ternary designs show significant power-delay product reductions; 49 % in the ternary full adder and 62 % in the ternary multiplier compared to the existing methodology. We have also compared the number of transistors in CMOS-based binary logic circuits and ternary device-based logic circuits We propose a methodology for using ternary values effectively in sequential logic. Proposed ternary D flip-flop is designed to normally operate in four-edges of a ternary clock signal. A quad-edge-triggered ternary D flip-flop (QETDFF) is designed with static gates using CNTFET. From HSPICE simulation results, we have confirmed that power-delay-product (PDP) of QETDFF is reduced by 82.31 % compared to state of the art ternary D flip-flop. We synthesize a ternary serial adder using QETDFF. PDP of the proposed ternary serial adder is reduced by 98.23 % compared to state of the art design.ope

Low Power Reversible Parallel Binary Adder/Subtractor

In recent years, Reversible Logic is becoming more and more prominent technology having its applications in Low Power CMOS, Quantum Computing, Nanotechnology, and Optical Computing. Reversibility plays an important role when energy efficient computations are considered. In this paper, Reversible eight-bit Parallel Binary Adder/Subtractor with Design I, Design II and Design III are proposed. In all the three design approaches, the full Adder and Subtractors are realized in a single unit as compared to only full Subtractor in the existing design. The performance analysis is verified using number reversible gates, Garbage input/outputs and Quantum Cost. It is observed that Reversible eight-bit Parallel Binary Adder/Subtractor with Design III is efficient compared to Design I, Design II and existing design.Comment: 12 pages,VLSICS Journa

Technology Mapping for Circuit Optimization Using Content-Addressable Memory

The growing complexity of Field Programmable Gate Arrays (FPGA's) is leading to architectures with high input cardinality look-up tables (LUT's). This thesis describes a methodology for area-minimizing technology mapping for combinational logic, specifically designed for such FPGA architectures. This methodology, called LURU, leverages the parallel search capabilities of Content-Addressable Memories (CAM's) to outperform traditional mapping algorithms in both execution time and quality of results. The LURU algorithm is fundamentally different from other techniques for technology mapping in that LURU uses textual string representations of circuit topology in order to efficiently store and search for circuit patterns in a CAM. A circuit is mapped to the target LUT technology using both exact and inexact string matching techniques. Common subcircuit expressions (CSE's) are also identified and used for architectural optimization---a small set of CSE's is shown to effectively cover an average of 96% of the test circuits. LURU was tested with the ISCAS'85 suite of combinational benchmark circuits and compared with the mapping algorithms FlowMap and CutMap. The area reduction shown by LURU is, on average, 20% better compared to FlowMap and CutMap. The asymptotic runtime complexity of LURU is shown to be better than that of both FlowMap and CutMap

Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a complete family of logical operators corresponding to all the one-argument logical connectives. Scaling-up to n-arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean functions is presented and a Reed-Muller decomposition for quantum logical gates is derived. The common control gates can be easily obtained by considering the logical correspondence between the control logic operator and the binary propositional logic operator. A new polynomial and exponential formulation of the Toffoli gate is presented. The method has parallels to quantum gate-T optimization methods using powers of multilinear operator polynomials. The method is then applied naturally to alphabets greater than two for multi-valued logical gates used for quantum Fourier transform, min-max decision circuits and multivalued adders