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Memristor-based Circuits for Performing Basic Arithmetic Operations

Farnood Merrikh-Bayat, Saeed Bagheri Shouraki

arXiv:1008.3452v2cs.AR

TL;DR

The paper addresses arithmetic on analog values usually represented by voltage or current, despite the difficulty of storing analog values in circuits. It programs memristors to represent operands and proposes circuits for basic arithmetic; a divider experiment is reported as precise. The authors conclude that the circuits are simple, with some more efficient than voltage- or current-based equivalents.

  • Problem

    Analog values are difficult to store in circuits, and conventional arithmetic represents operands by voltage or current rather than memristance.

    Source: §1 · p. 1, §3 · p. 2

  • Method

    The paper programs memristors to predetermined values and uses their memristances as operands in circuits for addition, subtraction, multiplication, and division.

    Source: §3 · pp. 2–3

  • Results

    The divider produced a result described as simple and precise for 520 divided by 416, whose expected value is 1.25.

    Source: §4 · p. 4

  • Takeaways & Limitations

    The authors conclude that the proposed circuits are simple and that some are more efficient than equivalent voltage- or current-based circuits.

    Source: §5 · p. 4, §3 · p. 4

    The circuit analysis assumes input amplitude or duration is small enough that it does not change memristance, allowing each memristor to be treated as a resistor.

    Source: §3 · p. 3

Abstract

from arXiv · show

In almost all of the currently working circuits, especially in analog circuits implementing signal processing applications, basic arithmetic operations such as multiplication, addition, subtraction and division are performed on values which are represented by voltages or currents. However, in this paper, we propose a new and simple method for performing analog arithmetic operations which in this scheme, signals are represented and stored through a memristance of the newly found circuit element, i.e. memristor, instead of voltage or current. Some of these operators such as divider and multiplier are much simpler and faster than their equivalent voltage-based circuits and they require less chip area. In addition, a new circuit is designed for programming the memristance of the memristor with predetermined analog value. Presented simulation results demonstrate the effectiveness and the accuracy of the proposed circuits.

1. Introduction

The paper proposes performing arithmetic on operands represented by memristance rather than voltage or current. It responds to the complexity of an earlier memristor-based approach and the difficulty of storing analog values in circuits.

1. Introduction

  • The proposed approach represents arithmetic operands by memristance instead of voltage or current.The introduction contrasts this with conventional signal representation and notes an earlier memristor-based arithmetic proposal was too complicated.Source: §1 · p. 1
  • Storing analog values in analog circuits is difficult, while analog arithmetic is described as faster than equivalent digital circuits.These points motivate an analog representation for arithmetic.Source: §1 · p. 1
  • The paper outlines memristor characteristics and analog storage, then programming and arithmetic circuits, experimental results, and conclusions.Source: §1 · p. 1

2. Interesting characteristics of memristor

A memristor’s resistance changes with applied bias, making it an analog variable resistor. The paper presents it as a way to store analog values as impedance rather than voltage.

2. Interesting characteristics of memristor

  • The memristor’s internal state determines the lengths of its low-resistance doped and high-resistivity undoped regions.The paper identifies the device structure as a semiconductor thin film between two metal contacts.Source: §2 · p. 2
  • Reversing current direction changes the direction of memristance adjustment, and longer current application changes resistance more.Current in one direction increases resistance; reversing it decreases resistance.Source: §2 · p. 2
  • Figure 1 depicts the memristor structure and its equivalent circuit model.Source: Figure 1 · p. 2
  • Memristance can store analog values as impedance instead of voltage.Source: §2 · p. 2

3. Basic arithmetic operations based on memristor

The paper programs memristors to predetermined values and uses those values as operands in circuits for basic arithmetic. The designs rely on memristance remaining effectively unchanged during operation.

3. Basic arithmetic operations based on memristor

  • A feedback circuit adjusts a memristor toward a predetermined resistance by changing current direction according to the sensed voltage.The resulting programmed memristor can then serve as an arithmetic operand.Source: §3 · pp. 2–3
  • Series-connected memristors add their resistances, subtraction uses a negative memristance, and op-amp circuits implement division and multiplication.The divider output is the memristance ratio when the amplifier gain is set to -1; input voltage or current can scale outputs to avoid op-amp saturation.Source: §3 · p. 3
  • The arithmetic analysis assumes input amplitude or duration is small enough not to change memristance, so each device acts as a resistor.Source: §3 · p. 3
  • The authors describe the divider as more efficient than its voltage-based equivalent and say memristor-stored values theoretically remain fixed indefinitely.They also connect memristor arithmetic to prospective hardware emulating neurons and synapses.Source: §3 · pp. 3–4

4. Experimental results

The reported experiment programs two memristors and uses them in a divider, whose output is presented as evidence of precise division.

4. Experimental results

  • 520 divided by 416 should equal 1.25; the programmed memristors produce a divider output the authors describe as simple and precise.The devices are adjusted to 520 Ω and 416 Ω, then used in the Fig. 3(c) divider with a -1 V narrow square-pulse input.Source: §4 · p. 4
  • The adjustment procedure is illustrated for memristances of 520 Ω and 416 Ω using a parameter value of 0.01.Figures 4(a) and 4(b) show voltage across the memristors during adjustment.Source: §4 · p. 4
  • Figure 4(c) presents the divider’s output voltage for the narrow square-pulse input.Source: §4 · p. 4

5. Conclusion

The paper proposes memristance-based arithmetic, a circuit for programming predetermined memristance values, and circuits that are simple, with some more efficient than voltage- or current-based equivalents.

  • The proposed method performs basic arithmetic operations on operands represented by memristance.Source: §5 · p. 4
  • A new circuit programs a memristor to a predetermined memristance value.Source: §5 · p. 4
  • The proposed circuits are simple, and some are more efficient than equivalent voltage- or current-based circuits.Source: §5 · p. 4
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