Arithmetic Operations in Multi-Valued Logic

This paper presents arithmetic operations like addition, subtraction and multiplications in Modulo-4 arithmetic, and also addition, multiplication in Galois field, using multi-valued logic (MVL). Quaternary to binary and binary to quaternary converters are designed using down literal circuits. Negation in modular arithmetic is designed with only one gate. Logic design of each operation is achieved by reducing the terms using Karnaugh diagrams, keeping minimum number of gates and depth of net in to consideration. Quaternary multiplier circuit is proposed to achieve required optimization. Simulation result of each operation is shown separately using Hspice.Comment: 12 Pages, VLSICS Journal 201

Power Optimization of Combinational Quaternary Logic Circuits

Design of the binary logic circuits is restricted by the need of the interconnections. Interconnections increase delay, area and energy consumption in CMOS digital circuits. A possible solution could be here at by using a bigger set of signals over the same chip area. Multiple-valued logic can decrease the average power required for level transitions and reduces the number of necessary interconnections. In this paper we design various combinational circuits using quaternary logic. Various combinational circuit such as multi valued logic full adder using unique encoding technique, quaternary encoder and quaternary multiplexer. This design is target to reduce the transistor used to implement the circuit and dropping the power dissipation. Power optimization is achieved using MTCMOS technique. Simulation has been done in Tanner 13 EDA tool on BSIM3 180 nm CMOS Technology. DOI: 10.17762/ijritcc2321-8169.15026

Low-Power Heterogeneous Graphene Nanoribbon-CMOS Multistate Volatile Memory Circuit

Graphene is an emerging nanomaterial believed to be a potential candidate for post-Si nanoelectronics, due to its exotic properties. Recently, a new graphene nanoribbon crossbar (xGNR) device was proposed which exhibits negative differential resistance (NDR). In this paper, a multi-state memory design is presented that can store multiple bits in a single cell enabled by this xGNR device, called Graphene Nanoribbon Tunneling Random Access Memory (GNTRAM). An approach to increase the number of bits per cell is explored alternative to physical scaling to overcome CMOS SRAM limitations. A comprehensive design for quaternary GNTRAM is presented as a baseline, implemented with a heterogeneous integration between graphene and CMOS. Sources of leakage and approaches to mitigate them are investigated. This design is extensively benchmarked against 16nm CMOS SRAMs and 3T DRAM. The proposed quaternary cell shows up to 2.27x density benefit vs. 16nm CMOS SRAMs and 1.8x vs. 3T DRAM. It has comparable read performance and is power-efficient, up to 1.32x during active period and 818x during stand-by against high performance SRAMs. Multi-state GNTRAM has the potential to realize high-density low-power nanoscale embedded memories. Further improvements may be possible by using graphene more extensively, as graphene transistors become available in future

Comparison of Binary and Multi-Level Logic Electronics for Embedded Systems

Embedded systems are dependent on low-power, miniaturized instrumentation. Comparator circuits are common elements in applications for digital threshold detection. A multi-level, memory-based logic approach is in development that offers potential benefits in power usage and size with respect to traditional binary logic systems. Basic 4-bit operations with CMOS gates and comparators are chosen to compare circuit implementations of binary structures and quaternary equivalents. Circuit layouts and functional operation are presented. In particular, power characteristics and transistor count are examined. The potential for improved embedded systems based on the multilevel, memory-based logic is discussed

Multi-Valued Majority Logic Circuits Using Spin Waves

With increasing data sets for processing, there is a requirement to build faster and smaller arithmetic circuits. One of the ways to improve the performance of higher order arithmetic units is to reduce the carry propagation levels. Multi-valued logic enables this by reducing the number of digits required to represent a range of numbers. Area reduction is also obtained through fewer operations and signals required to realise a function. Though theoretically multi-valued logic has these advantages, implementation of the multi-valued logic using CMOS has not been efficient. The main reason is because multi-valued logic is emulated in CMOS using binary switches. Two main approaches are followed in CMOS in implementing multi-valued logic using CMOS. Voltage mode logic, where the logic states are encoded using the node voltages suffer from low noise margins and limitation of radix due to the power supply. Current mode logic, where the branch currents are used to represent the logic levels suffer from high power consumption due to static current flow and requirement of restoration devices. The mindset of the post-CMOS approaches explored so far for multi-valued logic circuit design has been to replace the CMOS switches with their novel nano switches. Hence they too suffer from the same issues as CMOS implementation. Our value proposition is through the use of a truly multi-state device based on electron spin. Spin waves, which are a collection of electron spins of an atom enables multi-valued logic by allowing encoding information in the amplitude and phase of the wave.Another advantage of the spin wave fabric is that the computation is through wave propagation and interference which does not involve any movement of charge. This enables building low energy,smaller and faster multi-valued circuits. In this thesis, implementation of the basic building blocks of multi-valued logic using these novel spin wave based devices is shown. Building of arithmetic circuits like adders using these building blocks have also been demonstrated. To quantify the benefits of spin wave based multi-valued circuits, they are benchmarked with CMOS. For 32-bits, our projected comparisons show a 5X increased performance, 125X area improvement and 1717X power reduction for hexa-decimal spin wave based adders compared to binary CMOS. Similarly there is a 4X increase in performance of hexa-decimal SPWF multiplier compared to CMOS for 16 bits. Finally, we have implemented the I/O circuits for smooth interface between binary CMOS and multi-valued SPWF logic

Ternary and quaternary logic to binary bit conversion CMOS integrated circuit design using multiple input floating gate MOSFETs

Multiple-input floating gate MOSFETs and floating gate potential diagrams have been used for conversion of ternary-valued input and quaternary-valued input into corresponding binary-valued output in CMOS integrated circuit design environment. The method is demonstrated through the design of a circuit for conversion of ternary inputs 00 to -1-1 (decimal 0 to -4) and 00 to 11 (decimal 0 to +4) into the corresponding binary bits and for conversion of quaternary inputs (decimal 0 to 3) into the corresponding binary bits (binary 00 to 11) in a standard 1.5 mm digital CMOS technology. The physical design of the circuits is simulated and tested with SPICE using MOSIS BSIM3 model parameters. The conversion method is simple and compatible with the present CMOS process. The circuits could be embedded in digital CMOS VLSI design architectures. The conversion circuit for ternary inputs into corresponding binary outputs has maximum propagation delay of 8 ns with 0.1 pF simulated capacitive load. The physical layout design occupies an area of 432´908 mm2. The conversion circuit for quaternary inputs to corresponding binary outputs has maximum propagation delay of 6 ns with 0.1 pF simulated capacitive load. The physical layout design occupies an area of 130´175 mm2. The conversion circuit achieved significant improvement in the number of devices. A reduction of more than 75% in transistor count was obtained over the previous designs. Measurements of the fabricated devices for the conversion of quaternary input into binary output agree with simulated values