scholarly journals Fan-out enabled spin wave majority gate

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Christoph Adelmann ◽  
Florin Ciubotaru ◽  
Said Hamdioui ◽  
...  
Keyword(s):  
Spin Wave ◽  
State Of The Art ◽  
Logic Gate ◽  
Logic Circuits ◽  
Boolean Logic ◽  
Function Evaluation ◽  
Majority Gate ◽  
Logic Function ◽  
Micromagnetic Simulations ◽  
Majority Logic

By its very nature, Spin Wave (SW) interference provides intrinsic support for Majority logic function evaluation. Due to this and the fact that the 3-input Majority (MAJ3) gate and the Inverter constitute a universal Boolean logic gate set, different MAJ3 gate implementations have been proposed. However, they cannot be directly utilized for the construction of larger SW logic circuits as they lack a key cascading mechanism, i.e., fan-out capability. In this paper, we introduce a novel ladder-shaped SW MAJ3 gate design able to provide a maximum fan-out of 2 (FO2). The proper gate functionality is validated by means of micromagnetic simulations, which also demonstrate that the amplitude mismatch between the two outputs is negligible proving that an FO2 is properly achieved. Additionally, we evaluate the gate area and compare it with SW state-of-the-art and 15nm CMOS counterparts working under the same conditions. Our results indicate that the proposed structure requires 12x less area than the 15 nm CMOS MAJ3 gate and that at the gate level the fan-out capability results in 16% area savings, when compared with the state-of-the-art SW majority gate counterparts.

scholarly journals Fan-out enabled spin wave majority gate

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Christoph Adelmann ◽  
Florin Ciubotaru ◽  
Said Hamdioui ◽  
...  
Keyword(s):  
Spin Wave ◽  
State Of The Art ◽  
Logic Gate ◽  
Logic Circuits ◽  
Boolean Logic ◽  
Function Evaluation ◽  
Majority Gate ◽  
Logic Function ◽  
Micromagnetic Simulations ◽  
Majority Logic

By its very nature, Spin Wave (SW) interference provides intrinsic support for Majority logic function evaluation. Due to this and the fact that the 3-input Majority (MAJ3) gate and the Inverter constitute a universal Boolean logic gate set, different MAJ3 gate implementations have been proposed. However, they cannot be directly utilized for the construction of larger SW logic circuits as they lack a key cascading mechanism, i.e., fan-out capability. In this paper, we introduce a novel ladder-shaped SW MAJ3 gate design able to provide a maximum fan-out of 2 (FO2). The proper gate functionality is validated by means of micromagnetic simulations, which also demonstrate that the amplitude mismatch between the two outputs is negligible proving that an FO2 is properly achieved. Additionally, we evaluate the gate area and compare it with SW state-of-the-art and 15nm CMOS counterparts working under the same conditions. Our results indicate that the proposed structure requires 12x less area than the 15 nm CMOS MAJ3 gate and that at the gate level the fan-out capability results in 16% area savings, when compared with the state-of-the-art SW majority gate counterparts.

scholarly journals Fanout of 2 Triangle Shape Spin Wave Logic Gates

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Florin Ciubotaru ◽  
Christoph Adelmann ◽  
Sorin Cotofana ◽  
...  
Keyword(s):  
Spin Wave ◽  
State Of The Art ◽  
Logic Gates ◽  
The Other ◽  
Energy Reduction ◽  
Phase Detection ◽  
Majority Gate ◽  
Xor Gate ◽  
Micromagnetic Simulations ◽  
Threshold Detection

Having multi-output logic gates saves much energy because the same structure can be used to feed multiple inputs of next stage gates simultaneously. This paper proposes novel triangle shape fanout of 2 spin wave Majority and XOR gates; the Majority gate is achieved by phase detection, whereas the XOR gate is achieved by threshold detection. The proposed logic gates are validated by means of micromagnetic simulations. Furthermore, the energy and delay are estimated for the proposed structures and compared with the state-of-the-art spin wave logic gates, and 16nm and 7nm CMOS. The results demonstrate that the proposed structures provide energy reduction of 25%-50% in comparison to the other 2-output spin-wave devices while having the same delay, and energy reduction between 43x and 0.8x when compared to the 16nm and 7nm CMOS while having delay overhead between 11x and 40x.

scholarly journals Fanout of 2 Triangle Shape Spin Wave Logic Gates

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Florin Ciubotaru ◽  
Christoph Adelmann ◽  
Sorin Cotofana ◽  
...  
Keyword(s):  
Spin Wave ◽  
State Of The Art ◽  
Logic Gates ◽  
The Other ◽  
Energy Reduction ◽  
Phase Detection ◽  
Majority Gate ◽  
Xor Gate ◽  
Micromagnetic Simulations ◽  
Threshold Detection

Having multi-output logic gates saves much energy because the same structure can be used to feed multiple inputs of next stage gates simultaneously. This paper proposes novel triangle shape fanout of 2 spin wave Majority and XOR gates; the Majority gate is achieved by phase detection, whereas the XOR gate is achieved by threshold detection. The proposed logic gates are validated by means of micromagnetic simulations. Furthermore, the energy and delay are estimated for the proposed structures and compared with the state-of-the-art spin wave logic gates, and 16nm and 7nm CMOS. The results demonstrate that the proposed structures provide energy reduction of 25%-50% in comparison to the other 2-output spin-wave devices while having the same delay, and energy reduction between 43x and 0.8x when compared to the 16nm and 7nm CMOS while having delay overhead between 11x and 40x.

scholarly journals Fanout of 2 Triangle Shape Spin Wave Logic Gates

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Florin Ciubotaru ◽  
Christoph Adelmann ◽  
Sorin Cotofana ◽  
...  
Keyword(s):  
Spin Wave ◽  
State Of The Art ◽  
Logic Gates ◽  
The Other ◽  
Energy Reduction ◽  
Phase Detection ◽  
Majority Gate ◽  
Xor Gate ◽  
Micromagnetic Simulations ◽  
Threshold Detection

Having multi-output logic gates saves much energy because the same structure can be used to feed multiple inputs of next stage gates simultaneously. This paper proposes novel triangle shape fanout of 2 spin wave Majority and XOR gates; the Majority gate is achieved by phase detection, whereas the XOR gate is achieved by threshold detection. The proposed logic gates are validated by means of micromagnetic simulations. Furthermore, the energy and delay are estimated for the proposed structures and compared with the state-of-the-art spin wave logic gates, and 16nm and 7nm CMOS. The results demonstrate that the proposed structures provide energy reduction of 25%-50% in comparison to the other 2-output spin-wave devices while having the same delay, and energy reduction between 43x and 0.8x when compared to the 16nm and 7nm CMOS while having delay overhead between 11x and 40x.

scholarly journals Spin Wave Based Approximate 4:2 Compressor

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Florin Ciubotaru ◽  
Christoph Adelmann ◽  
Said Hamdioui ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Error Rate ◽  
Energy Efficient ◽  
Directional Coupler ◽  
State Of The Art ◽  
The Other ◽  
Average Error ◽  
Majority Gate ◽  
Micromagnetic Simulations ◽  
Average Error Rate

In this paper, we propose an energy efficient SW based approximate 4:2 compressor comprising a 3-input and a 5-input Majority gate. We validate our proposal by means of micromagnetic simulations, and assess and compare its performance with one of the state-of-the-art SW, 45nm CMOS, and Spin-CMOS counterparts. The evaluation results indicate that the proposed compressor consumes 31.5\% less energy in comparison with its accurate SW design version. Furthermore, it has the same energy consumption and error rate as the approximate compressor with Directional Coupler (DC), but it exhibits 3x lower delay. In addition, it consumes 14% less energy, while having 17% lower average error rate than the approximate 45nm CMOS counterpart. When compared with the other emerging technologies, the proposed compressor outperforms approximate Spin-CMOS based compressor by 3 orders of magnitude in term of energy consumption while providing the same error rate. Finally, the proposed compressor requires the smallest chip real-estate measured in terms of devices.

Logic Devices with Spin Wave Buses - an Approach to Scalable Magneto-Electric Circuitry

2008 ◽  
Vol 1067 ◽  
Author(s):  
Alexander Khitun ◽  
Mingqiang Bao ◽  
Yina Wu ◽  
Ji-Young Kim ◽  
Augustin Hong ◽  
...  
Keyword(s):  
Spin Wave ◽  
Room Temperature ◽  
Logic Gate ◽  
Logic Gates ◽  
Logic Circuits ◽  
Logic Device ◽  
Logic Devices ◽  
Magnetic Circuits ◽  
Micrometer Scale ◽  
Magnetization Signal

ABSTRACTWe analyze spin wave-based logic circuits as a possible route to building reconfigurable magnetic circuits compatible with conventional electron-based devices. A distinctive feature of the spin wave logic circuits is that a bit of information is encoded into the phase of the spin wave. It makes possible to transmit information as a magnetization signal through magnetic waveguides without the use of an electric current. By exploiting sin wave superposition, a set of logic gates such as AND, OR, and Majority gate can be realized in one circuit. We present experimental data illustrating the performance of a three-terminal micrometer scale spin wave-based logic device fabricated on a silicon platform. The device operates in the GHz frequency range and at room temperature. The output power modulation is achieved via the control of the relative phases of two input spin wave signals. The obtained data shows the possibility of using spin waves for achieving logic functionality. The scalability of the spin wave-based logic devices is defined by the wavelength of the spin wave, which depends on the magnetic material and waveguide geometry. Potentially, a multifunctional spin wave logic gate can be scaled down to 0.1μm2. Another potential advantage of the spin wave-based logic circuitry is the ability to implement logic gates with fewer elements as compared to CMOS-based circuits in achieving same functionality. The shortcomings and disadvantages of the spin wave-based devices are also discussed.

scholarly journals 2-output Spin Wave Programmable Logic Gate

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Christoph Adelmann ◽  
Florin Ciubotaru ◽  
Sorin Cotofana ◽  
...  
Keyword(s):  
Spin Wave ◽  
Boolean Functions ◽  
State Of The Art ◽  
Logic Gate ◽  
Object Oriented ◽  
Programmable Logic ◽  
Area Reduction ◽  
Gate Structure ◽  
Cmos Implementation ◽  
Practical Implications

This paper presents a 2-output Spin-Wave Programmable Logic Gate structure able to simultaneously evaluate any pair of AND, NAND, OR, NOR, XOR, and XNOR Boolean functions. Our proposal provides the means for fanout achievement within the Spin Wave computation domain and energy and area savings as two different functions can be simultaneously evaluated on the same input data. We validate our proposal by means of Object Oriented Micromagnetic Framework (OOMMF) simulations and demonstrate that by phase and magnetization threshold output sensing \{AND, OR, NAND, NOR\} and \{XOR and XNOR\} functionalities can be achieved, respectively. To get inside into the potential practical implications of our approach we use the proposed gate to implement a 3-input Majority gate, which we evaluate and compare with state of the art equivalent implementations in terms of area, delay, and energy consumptions. Our estimations indicate that the proposed gate provides 33% and 16% energy and area reduction, respectively, when compared with spin-wave counterpart and 42% energy reduction while consuming 12x less area when compared to a 15 nm CMOS implementation.

scholarly journals Rediscovering Majority Logic in the Post-CMOS Era: A Perspective from In-Memory Computing

2020 ◽  
Vol 10 (3) ◽  
pp. 28
Author(s):  
John Reuben
Keyword(s):  
Integrated Circuits ◽  
Logic Gates ◽  
Expressive Power ◽  
Boolean Logic ◽  
Majority Gate ◽  
Von Neumann ◽  
Majority Logic ◽  
Memory Array ◽  
Memory Wall ◽  
Parallel Prefix

As we approach the end of Moore’s law, many alternative devices are being explored to satisfy the performance requirements of modern integrated circuits. At the same time, the movement of data between processing and memory units in contemporary computing systems (‘von Neumann bottleneck’ or ‘memory wall’) necessitates a paradigm shift in the way data is processed. Emerging resistance switching memories (memristors) show promising signs to overcome the ‘memory wall’ by enabling computation in the memory array. Majority logic is a type of Boolean logic which has been found to be an efficient logic primitive due to its expressive power. In this review, the efficiency of majority logic is analyzed from the perspective of in-memory computing. Recently reported methods to implement majority gate in Resistive RAM array are reviewed and compared. Conventional CMOS implementation accommodated heterogeneity of logic gates (NAND, NOR, XOR) while in-memory implementation usually accommodates homogeneity of gates (only IMPLY or only NAND or only MAJORITY). In view of this, memristive logic families which can implement MAJORITY gate and NOT (to make it functionally complete) are to be favored for in-memory computing. One-bit full adders implemented in memory array using different logic primitives are compared and the efficiency of majority-based implementation is underscored. To investigate if the efficiency of majority-based implementation extends to n-bit adders, eight-bit adders implemented in memory array using different logic primitives are compared. Parallel-prefix adders implemented in majority logic can reduce latency of in-memory adders by 50–70% when compared to IMPLY, NAND, NOR and other similar logic primitives.

scholarly journals 2-output Spin Wave Programmable Logic Gate

2021 ◽  
Author(s):  
Abdulqader Mahmoud ◽  
Frederic Vanderveken ◽  
Christoph Adelmann ◽  
Florin Ciubotaru ◽  
Sorin Cotofana ◽  
...  
Keyword(s):  
Spin Wave ◽  
Boolean Functions ◽  
State Of The Art ◽  
Logic Gate ◽  
Object Oriented ◽  
Programmable Logic ◽  
Area Reduction ◽  
Gate Structure ◽  
Cmos Implementation ◽  
Practical Implications

This paper presents a 2-output Spin-Wave Programmable Logic Gate structure able to simultaneously evaluate any pair of AND, NAND, OR, NOR, XOR, and XNOR Boolean functions. Our proposal provides the means for fanout achievement within the Spin Wave computation domain and energy and area savings as two different functions can be simultaneously evaluated on the same input data. We validate our proposal by means of Object Oriented Micromagnetic Framework (OOMMF) simulations and demonstrate that by phase and magnetization threshold output sensing \{AND, OR, NAND, NOR\} and \{XOR and XNOR\} functionalities can be achieved, respectively. To get inside into the potential practical implications of our approach we use the proposed gate to implement a 3-input Majority gate, which we evaluate and compare with state of the art equivalent implementations in terms of area, delay, and energy consumptions. Our estimations indicate that the proposed gate provides 33% and 16% energy and area reduction, respectively, when compared with spin-wave counterpart and 42% energy reduction while consuming 12x less area when compared to a 15 nm CMOS implementation.

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