Memristor-Based Volistor Gates Compute Logic with Low Power Consumption

We introduce a novel volistor logic gate which uses voltage as input and resistance as output. Volistors rely on the diode-like behavior of rectifying memristors. We show how to realize the first logic level, counted from the input, of any Boolean function with volistor gates in a memristive crossbar network. Unlike stateful logic, there is no need to store the inputs as resistances, and computation is performed directly. The fan-in and fan-out of volistor gates are large and different from traditional memristor circuits. Compared to solely memristive stateful logic, a combination of volistors and stateful inhibition gates can significantly reduce the number of operations required to calculate arbitrary multi-output Boolean functions. The power consumption of volistor logic is computed and compared with the power consumption of stateful logic using the simulation results obtained by LTspice—when implemented in a 1 × 8 or an 8 × 1 crosspoint array, volistors consume significantly less power

New Approaches for Memristive Logic Computations

Over the past five decades, exponential advances in device integration in microelectronics for memory and computation applications have been observed. These advances are closely related to miniaturization in integrated circuit technologies. However, this miniaturization is reaching the physical limit (i.e., the end of Moore\u27s Law). This miniaturization is also causing a dramatic problem of heat dissipation in integrated circuits. Additionally, approaching the physical limit of semiconductor devices in fabrication process increases the delay of moving data between computing and memory units hence decreasing the performance. The market requirements for faster computers with lower power consumption can be addressed by new emerging technologies such as memristors. Memristors are non-volatile and nanoscale devices and can be used for building memory arrays with very high density (extending Moore\u27s law). Memristors can also be used to perform stateful logic operations where the same devices are used for logic and memory, enabling in-memory logic. In other words, memristor-based stateful logic enables a new computing paradigm of combining calculation and memory units (versus von Neumann architecture of separating calculation and memory units). This reduces the delays between processor and memory by eliminating redundant reloading of reusable values. In addition, memristors consume low power hence can decrease the large amounts of power dissipation in silicon chips hitting their size limit. The primary focus of this research is to develop the circuit implementations for logic computations based on memristors. These implementations significantly improve the performance and decrease the power of digital circuits. This dissertation demonstrates in-memory computing using novel memristive logic gates, which we call volistors (voltage-resistor gates). Volistors capitalize on rectifying memristors, i.e., a type of memristors with diode-like behavior, and use voltage at input and resistance at output. In addition, programmable diode gates, i.e., another type of logic gates implemented with rectifying memristors are proposed. In programmable diode gates, memristors are used only as switches (unlike volistor gates which utilize both memory and switching characteristics of the memristors). The programmable diode gates can be used with CMOS gates to increase the logic density. As an example, a circuit implementation for calculating logic functions in generalized ESOP (Exclusive-OR-Sum-of-Products) form and multilevel XOR network are described. As opposed to the stateful logic gates, a combination of both proposed logic styles decreases the power and improves the performance of digital circuits realizing two-level logic functions Sum-of-Products or Product-of-Sums. This dissertation also proposes a general 3-dimentional circuit architecture for in-memory computing. This circuit consists of a number of stacked crossbar arrays which all can simultaneously be used for logic computing. These arrays communicate through CMOS peripheral circuits

A Time-Efficient CMOS-Memristive Programmable Circuit Realizing Logic Functions in Generalized AND-XOR Structures

This paper describes a CMOS-memristive Programmable Logic Device connected to CMOS XOR gates (mPLD-XOR) for realizing multi-output functions well-suited for two-level {NAND, AND, NOR, OR}-XOR based design. This structure is a generalized form of AND-XOR logic where any combination of NAND, AND, NOR, OR, and literals can replace the AND level. For mPLD-XOR, the computational delay, which is measured as the number of clock cycles, equals the maximum number of inputs to any output XOR gate of a function assuming that the number of XOR gates is large enough to calculate the outputs of the function simultaneously. The input levels of functions are implemented with novel programmable diode gates, which rely on the diode-like behavior of self-rectifying memristors, and the output levels of functions are realized with CMOS modulo-two counters. As an example, the circuit implementation of a 3-bit adder and a 3-bit multiplier are presented. The size and performance of the implemented circuits are estimated and compared with that of the equivalent circuits realized with stateful logic gates. Adding a feedback circuit to the mPLD-XOR allows the implementation of a multilevel XOR logic network with any combination of sums, products, XORs, and literals at the input of any XOR gate. The mPLD-XOR with feedback can reduce the size and number of computational steps (clock cycles) in realizing logic functions, which makes it well suited for use in communication and parallel computing systems where fast arithmetic operations are demanding

Survey on the Benefits of Using Memristors for Pufs

This paper reviews memristive PUFs (Physical Unclonable Functions) reported in the literature. The paper explains the motivation for using memristor technology for implementing PUFs. It focuses on PUFs’ applications, sizes, analysis, and physical variations. In addition, the paper presents the number of samples generated using Monte Carlo simulation for evaluating the PUF circuits. This paper also describes the protocols, functionality, and methodologies proposed in the memristive PUF literature. Although memristive PUFs are not commercialized yet, there is a high expectation of exploiting the memristors as fundamental elements in the next generation of hardware security primitives (e.g. PUF) due to their unique characteristics such as forming process, temporal drift, nonlinearity, bidirectionality, nonvolatility and model complexity. There have been some survey papers on memristor PUFs in the past, however, the field has continued to develop so a comprehensive survey including recent publications seemed in order at this time. Lately, memristor technology improvement has accelerated, therefore creating a need for an updated survey of the applications of memristors for PUFs

A 3D Crossbar Architecture for both Pipeline and Parallel Computations

A 3D architecture made up of a CMOS layer combined with a 3D stack of bipolar memristor crossbar arrays provides an innovative approach to hardware support for utilizing the strength of CMOS combined with the strength of memristors. Memristors have been evaluated for implementing a broad spectrum of applications such as memory, computations, hardware-based security primitives, cryptography, etc., and numerous studies have shown that memristors are desirable candidates for such applications. This paper proposes a novel 3D memristive crossbar architecture (i.e., a stack of memristive crossbar arrays built on top of CMOS substrate) with a specific focus on the way of connecting the crossbar arrays to the CMOS layer. The proposed architecture is configurable and allows restructuring crossbar arrays and creating 1D arrays with adjustable sizes. The proposed architecture enables parallel and pipeline computations where data can move or be processed in planes perpendicular to the stacked crossbar arrays. In addition, the proposed architecture is scalable meaning that stacks of crossbar arrays can be connected without additional overhead. This paper shows examples of implementing a full adder, a 4-bit look-ahead carry generator, and an 8-bit multiplexer. Simulations and area, delay, and power analysis demonstrate the behavior of the proposed 3D circuit

Multi-input Volistor Logic XNOR Gates

A novel approach utilising the emerging memristor technology is introduced for realising a 2-input primitive XNOR gate. This gate enables in-memory computing and is used as a building block of multi-input XNOR gates. The XNOR gate is realised with eight memristors of two crossbar arrays. The average power consumption of an 8-input XNOR gate is calculated and compared with its counterpart realised with CMOS technology – the XNOR gate consumes less power. ESOP realisation can be directly implemented with XNOR gates. Our simulation results and comparisons show the benefit of the proposed XNOR gate in terms of delay, area, and power. Volistor logic XNOR gate. (a) Circuit diagram of two-input volistor logic XNOR gate. Input voltages are applied to memristors S1 and S2 through horizontal wires Win1 and Win2, and the output which is logical AND of states S1 and S2 is calculated by applying VREAD to vertical wire WXNOR. (b) Block diagram of two-input volistor logic gate. (c) A multi-input volistor logic XNOR gate can be implemented by connecting two XNOR gates though CMOS switches