Electronics Guide

Mathematical Background

Binary logic operates on the Boolean algebra developed by George Boole in the mid-nineteenth century, where variables take values from the set {0, 1} and operations include AND, OR, and NOT. Multi-valued logic generalizes this framework to sets with more than two elements, requiring new definitions for logical operations and new algebraic structures to describe their behavior.

Post algebras, introduced by Emil Post in the 1920s, provide one mathematical framework for multi-valued logic. In a Post algebra with n values, signals can take any value from the set {0, 1, 2, ..., n-1}. Operations generalize from binary logic: a generalized NOT operation might cycle through values, while AND and OR operations might compute minimum and maximum values respectively. Alternative algebraic structures include Lukasiewicz algebras, which emphasize different properties, and various lattice-based formulations.

The choice of algebraic framework affects which operations are natural and efficient to implement. Binary Boolean algebra benefits from the correspondence between AND/OR operations and series/parallel switch networks. Multi-valued systems must find analogous physical implementations, which influences the practical viability of different algebraic choices.

Radix and Information Density

The radix or base of a number system determines how many symbols are available for each digit position. Binary uses radix 2, ternary uses radix 3, quaternary uses radix 4, and so on. Higher radices encode more information per digit: a single ternary digit (trit) carries log2(3) approximately 1.58 bits of information, while a quaternary digit carries exactly 2 bits.

This increased information density per signal potentially reduces the number of wires needed to communicate a given amount of information. A 32-bit address requires 32 binary wires but only 21 ternary wires or 16 quaternary wires. For systems where interconnect represents a significant constraint, whether in pin count, routing congestion, or transmission line complexity, this reduction can prove valuable.

However, the advantage of higher radix diminishes as radix increases. The optimal radix for minimizing the product of digit count and radix, a measure relevant to some implementation costs, is the mathematical constant e (approximately 2.718). This suggests ternary logic (radix 3) offers a theoretical optimum, though practical considerations often favor binary or quaternary implementations.

Noise Margins and Signal Integrity

A fundamental challenge for multi-valued logic is maintaining adequate noise margins as the number of logic levels increases. In binary systems, the voltage range between power supply rails divides into two regions separated by substantial margins. A 3.3V binary system might define logic low as 0-0.8V and logic high as 2.0-3.3V, providing 1.2V of noise margin.

With more logic levels, the available voltage range divides into more regions with smaller separations. A quaternary system using the same 3.3V supply might allocate approximately 0.8V per level with margins of only 0.3-0.4V. This reduced margin makes the system more susceptible to noise, crosstalk, and other signal integrity issues.

Maintaining reliable operation with reduced noise margins requires more careful circuit design, better signal integrity management, and often reduced operating speeds. These practical constraints have historically limited multi-valued logic adoption despite its theoretical advantages.

Standard Ternary

Standard ternary logic uses three values typically designated as 0, 1, and 2. Logical operations generalize from binary in various ways. The MIN and MAX functions serve as generalizations of AND and OR: MIN(a,b) returns the smaller of two values, while MAX(a,b) returns the larger. A simple NOT operation might compute (2-x), mapping 0 to 2, 1 to 1, and 2 to 0.

Arithmetic in standard ternary follows familiar patterns. Addition proceeds digit by digit with carries, where the sum of two ternary digits can produce a result from 0 to 4, potentially generating a carry. Multiplication tables are slightly larger than binary but follow similar principles. The representation of negative numbers requires conventions analogous to binary's two's complement.

Standard ternary finds application in some communication systems where three-level signaling increases throughput over binary channels. The USB 3.0 specification, for example, uses three-level pulse amplitude modulation (PAM-3) for its SuperSpeed signaling, encoding data more efficiently than binary signaling at the cost of more complex receiver circuits.

Balanced Ternary

Balanced ternary uses the values {-1, 0, +1} rather than {0, 1, 2}, providing a symmetric representation around zero. This seemingly minor change profoundly affects arithmetic properties, eliminating the need for separate sign representation and simplifying many operations.

In balanced ternary, negative numbers require no special representation: the negation of any number is obtained simply by negating each digit. The number five, represented as (+1, +1, -1) meaning 9 - 3 - 1, negates to (-1, -1, +1) or -5. This symmetry eliminates the complexities of two's complement arithmetic and the asymmetric range of signed binary representations.

Rounding to the nearest integer occurs naturally in balanced ternary through truncation. The fractional part of a balanced ternary number, consisting of digits with negative positional weights, truncates to zero by simply removing those digits. This provides banker's rounding (round half to even) behavior without additional logic.

The Soviet Setun computer, developed at Moscow State University in 1958, successfully implemented balanced ternary arithmetic. Its designers, led by Nikolai Brusentsov, found that balanced ternary simplified arithmetic circuits and provided elegant handling of signed numbers. Though production ceased in the 1960s, the Setun demonstrated that non-binary computation could work reliably in practice.

Ternary Logic Gates

Implementing ternary logic gates requires circuits capable of distinguishing and generating three voltage levels. Various approaches have been explored, each with different trade-offs between complexity, speed, and power consumption.

Resistor-transistor approaches use voltage dividers to create intermediate levels. A simple ternary inverter might use two transistors and two resistors, with the output voltage depending on which transistors conduct. While straightforward conceptually, resistor-based circuits consume static power and may suffer from process variation sensitivity.

Current-mode implementations represent logic values as current levels rather than voltages. Current-mode circuits can achieve higher speeds and better noise immunity in some implementations, as current signals are less susceptible to capacitive loading effects. Multiple-valued current-mode logic (MVCML) has been explored for high-speed applications where its advantages outweigh implementation complexity.

CMOS implementations of ternary logic typically use threshold detection circuits to distinguish three voltage levels and transmission gates or multiple transistor stacks to generate outputs. While more complex than binary CMOS, practical ternary CMOS circuits have been demonstrated in research implementations.

Ternary Memory

Storing ternary values requires memory cells capable of maintaining three distinct states. Various approaches have been explored, from modified SRAM cells with three stable states to multi-level flash memory operating in ternary mode.

Modified SRAM cells for ternary storage might use additional transistors to create a third stable state or employ asymmetric designs where intermediate voltage levels can be maintained. These cells typically require more transistors than binary SRAM, partially offsetting the density advantage of higher radix.

Flash memory naturally supports multiple levels through analog charge storage, and ternary operation represents a simpler variant of the multi-level cell (MLC) technology widely used in modern solid-state storage. Operating flash in ternary mode provides better reliability margins than higher-level operation while still improving density over binary.

Quaternary Fundamentals

Quaternary values typically designate as 0, 1, 2, and 3, corresponding directly to binary pairs 00, 01, 10, and 11. This mapping enables simple conversion between quaternary and binary representations: each quaternary digit expands to two binary digits, and each binary digit pair compresses to one quaternary digit.

Logical operations in quaternary can be defined in multiple ways. One approach treats quaternary values as pairs of binary values and applies binary operations component-wise. Alternative approaches define operations directly on the four-element set, with MIN and MAX again serving as natural generalizations of AND and OR.

The direct correspondence with binary makes quaternary attractive for communication systems where doubling information density per symbol without changing the underlying binary computation provides practical benefits. Several high-speed communication standards use four-level signaling (PAM-4) for this reason.

Quaternary in Communications

Modern high-speed serial interfaces increasingly employ quaternary signaling to achieve higher data rates without proportionally increasing symbol rates. PAM-4 (4-level pulse amplitude modulation) encodes two bits per symbol, enabling twice the data rate of binary signaling at the same symbol rate.

Ethernet standards for 200 Gbps and 400 Gbps data center applications specify PAM-4 signaling, as do PCI Express 6.0 and beyond. These applications accept the complexity of four-level signaling because doubling symbol rates to achieve equivalent throughput with binary signaling would face more severe channel limitations.

The receiver circuits for quaternary signaling require three threshold comparators rather than one, increasing complexity and power consumption. Equalization and signal conditioning become more critical as the voltage difference between adjacent levels decreases. Forward error correction helps maintain reliability despite reduced noise margins.

Quaternary Memory Applications

Multi-level cell (MLC) flash memory, storing two bits per cell, effectively operates as quaternary memory. The floating gate transistor maintains one of four charge levels, each corresponding to a two-bit value. This technology has become standard in consumer and enterprise solid-state storage.

The extension of flash memory to three bits per cell (TLC) and four bits per cell (QLC) continues this progression beyond quaternary, though reliability and endurance decrease with each additional level. The success of multi-level flash demonstrates that multi-valued storage can be commercially viable despite the challenges of distinguishing closely-spaced analog levels.

Research into quaternary DRAM explores storing four levels in each cell rather than two, potentially doubling memory density. The challenge lies in maintaining sufficient read margins while detecting small charge differences. Advances in sensing circuits and error correction may eventually enable practical quaternary DRAM.

Principles of Current-Mode Operation

In voltage-mode logic, signal values correspond to voltage levels referenced to a common ground. In current-mode logic, signal values correspond to current magnitudes flowing through circuit nodes. A ternary current-mode signal might use currents of 0, I, and 2I to represent values 0, 1, and 2.

Current signals offer several advantages for multi-valued logic. Currents sum naturally at circuit nodes, enabling simple implementation of addition and weighted sum operations. Current levels are less affected by capacitive loading than voltage levels, potentially enabling faster operation. Current signals can provide better common-mode noise rejection in differential implementations.

However, current-mode circuits typically consume more static power than voltage-mode CMOS, as maintaining current levels requires continuous power dissipation. Level conversion between current-mode and voltage-mode domains adds complexity at system interfaces. These trade-offs have limited current-mode adoption despite its advantages for certain applications.

Multiple-Valued Current-Mode Logic (MVCML)

MVCML extends current-mode logic techniques to multi-valued systems, using multiple current levels to encode information. Source-coupled transistor pairs steer current between outputs based on input voltage differences, with multiple pairs enabling multiple output current levels.

A ternary MVCML gate might use two differential pairs with different threshold voltages, steering current to different outputs depending on which thresholds the input exceeds. The output currents sum at load resistors to produce voltage levels corresponding to the ternary result.

MVCML has been explored for high-speed applications where its switching speed advantages offset power consumption concerns. Research implementations have demonstrated multi-GHz operation with ternary and quaternary signaling, suggesting applications in high-speed interconnects and communication interfaces.

Current-Mode Arithmetic

Current summation at circuit nodes naturally implements addition, making current-mode circuits attractive for arithmetic operations. Weighted sums, fundamental to digital signal processing and neural network computation, map directly to current combining with appropriately sized current sources.

A current-mode multiplier might use multiple current sources with binary-weighted magnitudes, enabling each source selectively based on multiplier bits. The sum of enabled currents represents the product. Multi-valued implementations extend this principle with current sources at multiple levels.

The analog nature of current summation provides natural support for multiply-accumulate operations central to many signal processing algorithms. This has motivated current-mode implementations of neural network accelerators, where approximate computation tolerance allows trading precision for efficiency.

Threshold Gate Fundamentals

A threshold gate computes a Boolean function by comparing a weighted sum of inputs against a threshold. Given inputs x1, x2, ..., xn with corresponding weights w1, w2, ..., wn and threshold T, the output is 1 if (w1*x1 + w2*x2 + ... + wn*xn) >= T and 0 otherwise.

Threshold gates can implement any linearly separable Boolean function in a single gate, while standard AND and OR gates implement only a subset of such functions. Functions requiring multiple levels of conventional gates may be realizable with a single threshold gate, potentially reducing circuit depth and delay.

The majority function, which outputs 1 when more than half of its inputs are 1, exemplifies threshold gate capability. A three-input majority requires either three AND/OR gates in a two-level implementation or a single threshold gate with equal weights and threshold 2. This reduction in gate count and levels motivates threshold logic exploration.

Multi-Valued Threshold Logic

Threshold logic extends naturally to multi-valued systems where both inputs and outputs can take multiple discrete values. A multi-valued threshold gate might partition its weighted sum range into multiple output regions, each producing a different output value.

For a ternary threshold gate, the weighted sum range divides into three regions separated by two thresholds. Sums below the first threshold produce output 0, sums between the thresholds produce output 1, and sums above the second threshold produce output 2. This single gate can implement functions that would require complex networks of binary or ternary standard gates.

The power of multi-valued threshold gates comes from combining the weighted sum capability of threshold logic with the increased information capacity of multi-valued signals. Research has explored both theoretical capabilities and practical implementations of these gates.

Implementation Approaches

Threshold gate implementation requires circuits that compute weighted sums and compare them against thresholds. Various technologies have been explored, from resistor networks and operational amplifiers to switched-capacitor circuits and memristive crossbar arrays.

Resistor-based implementations use resistor ratios to set weights, with comparators detecting threshold crossings. While conceptually simple, resistor matching requirements and temperature sensitivity present practical challenges. Active implementations using current mirrors provide better control over weight values.

Capacitor-based implementations store weights as capacitor ratios, using charge sharing to compute weighted sums. Switched-capacitor techniques enable programmable weights through capacitor array configurations. These approaches offer good matching in CMOS processes but require clock signals and have speed limitations.

Emerging memristive devices offer intriguing possibilities for threshold logic implementation. Memristor crossbar arrays naturally compute vector-matrix products, with programmable resistance values serving as weights. This structure implements threshold logic when combined with appropriate threshold detection circuitry.

Applications of Threshold Logic

Threshold logic finds particular application in pattern recognition and classification tasks, where weighted sum computation followed by thresholding mirrors the operation of biological neurons and artificial neural networks.

Image processing algorithms often employ threshold operations: edge detection, binarization, and morphological operations all involve comparing weighted combinations of pixel values against thresholds. Direct threshold logic implementation can prove more efficient than decomposing these operations into binary Boolean functions.

Sorting and ranking operations map naturally to threshold logic. Determining the median of a set of values, for instance, involves counting how many values exceed each candidate, a form of threshold computation. Multi-valued threshold gates can implement these comparisons efficiently.

Multi-Level Cell Technologies

Flash memory pioneered commercial multi-level cell (MLC) technology, storing two bits per cell by distinguishing four charge levels on floating gate transistors. This doubled density compared to single-level cell (SLC) flash with the same transistor size, though at some cost in speed and endurance.

The progression to triple-level cell (TLC, 3 bits per cell with 8 levels) and quad-level cell (QLC, 4 bits per cell with 16 levels) continues trading reliability margins for increased density. Modern solid-state drives use sophisticated error correction and signal processing to maintain acceptable reliability despite operating with closely-spaced voltage levels.

Programming multi-level cells requires precise charge placement, typically through iterative program-verify algorithms that incrementally add charge until the target level is reached. This precision requirement increases programming time compared to binary cells, contributing to lower write performance in high-density flash.

Sensing and Detection Challenges

Reading multi-valued memory cells requires distinguishing closely-spaced analog levels, a more challenging task than binary discrimination. Sense amplifiers must detect smaller voltage or current differences while maintaining acceptable error rates.

Reference cells or reference voltage generators provide comparison standards for level detection. In flash memory, reference cells programmed to intermediate levels define the boundaries between stored values. Reference accuracy and stability directly affect read reliability.

Statistical variation in programmed values, read disturb effects, and retention-related drift all blur the distinction between intended levels. Advanced signal processing techniques, including soft-decision decoding that considers analog level information rather than just digital decisions, help maintain reliability despite these challenges.

Emerging Multi-Valued Memory Technologies

Resistive RAM (ReRAM) and phase-change memory (PCM) store information as resistance states, with multiple resistance levels enabling multi-valued storage. These technologies offer potential advantages over flash for certain applications, including faster write speeds and better endurance.

ReRAM cells can be programmed to multiple resistance states by controlling the size or composition of conductive filaments within an insulating matrix. The analog nature of filament formation enables continuous resistance variation, though practical implementations typically define discrete levels to manage variability.

PCM exploits the resistance difference between crystalline and amorphous phases of chalcogenide materials, with intermediate crystallization states providing additional levels. The physics of crystallization enables more controlled intermediate state programming than some other technologies.

Research into multi-level MRAM (magnetoresistive RAM) explores using multiple magnetic states or analog resistance control to increase storage density. While MRAM's excellent endurance and speed make it attractive, achieving reliable multi-level operation adds complexity to an already challenging technology.

Error Correction for Multi-Valued Storage

Reliable multi-valued storage requires error correction tailored to the characteristics of multi-level cells. Errors may involve transitions to adjacent levels (the most common case) or larger jumps, with different probabilities for each error type.

Codes designed for multi-valued storage exploit the structure of level-based errors. Non-binary codes such as Reed-Solomon codes operating over finite fields with more than two elements naturally match multi-valued storage. Symbol-based rather than bit-based error handling aligns with the cell-level error behavior.

Soft-decision decoding uses analog information from the sensing process to improve decoding performance. Rather than making hard decisions about each cell's value, soft-decision decoders consider the probability distribution over possible values, enabling correction of more errors than hard-decision approaches.

Addition in Multi-Valued Systems

Multi-valued addition operates digit by digit with carry propagation, generalizing binary addition to higher radices. For radix r, the sum of two digits ranges from 0 to 2(r-1), potentially generating a carry to the next position.

A ternary full adder accepts two input trits and a carry-in trit, producing a sum trit and carry-out trit. The possible sum ranges from 0 to 6 (three inputs each ranging 0-2), which encodes as a carry of 0, 1, or 2 and a sum of 0, 1, or 2. This slightly more complex carry behavior compared to binary adds circuit complexity.

Carry-lookahead and other fast addition techniques adapt to multi-valued arithmetic with increased complexity. The wider range of carry values requires more elaborate propagate and generate logic than binary systems. Whether the reduced digit count compensates for increased per-stage complexity depends on specific implementation parameters.

Multiplication in Multi-Valued Systems

Multi-valued multiplication uses digit-by-digit partial product generation followed by accumulation, analogous to binary multiplication. Each partial product involves multiplying two single digits, with results ranging from 0 to (r-1)^2.

For ternary multiplication, single-digit products range from 0 to 4, requiring two trits for representation. The partial product array has fewer rows than binary for the same precision, but each entry is larger. Whether overall complexity decreases depends on how efficiently the larger digit products can be generated.

Lookup table approaches for multi-valued multiplication store precomputed products for all digit pair combinations. A ternary single-digit multiplication table has 9 entries (3x3), compared to 4 for binary. For quaternary, 16 entries are needed. As radix increases, table size grows quadratically, eventually favoring computational approaches over lookup.

Division and Other Operations

Division in multi-valued systems follows sequential digit-by-digit algorithms similar to binary division, with each step determining one quotient digit through comparison and subtraction. The wider digit range potentially enables faster convergence in Newton-Raphson and similar iterative division algorithms.

Comparison operations determine relative magnitude of multi-valued numbers through digit-by-digit analysis from most significant to least significant, identical in principle to binary comparison. Implementation details differ due to multi-level signal representation.

Shift operations in multi-valued systems multiply or divide by powers of the radix. A ternary left shift multiplies by 3, inserting a zero digit at the right. This radix-dependent behavior affects algorithm design when porting binary algorithms to multi-valued systems.

Manufacturing and Process Considerations

Standard semiconductor processes optimize for binary CMOS operation, with threshold voltages, operating voltages, and design rules tuned for two-level signaling. Multi-valued circuits using these processes must work within parameters not designed for their needs.

Multi-level voltage signaling demands better voltage reference accuracy than binary systems. Process variation that causes acceptable binary threshold shifts may push multi-valued levels into incorrect regions. Tighter process control or calibration techniques may be required.

Testing multi-valued circuits adds complexity beyond binary testing. Fault models must consider incorrect level generation as well as stuck-at faults. Test pattern generation must exercise all level transitions and combinations, increasing test time and complexity.

Interface and Compatibility

Multi-valued subsystems must interface with the predominantly binary digital world. Conversion circuits at boundaries add overhead that may offset internal advantages for small multi-valued regions.

Standard interfaces, memory buses, and communication protocols assume binary signaling. Using multi-valued logic internally while maintaining binary external interfaces limits the scope of multi-valued advantage. New standards explicitly supporting multi-valued signaling, such as PAM-4 for high-speed serial links, enable broader deployment.

Software tools, synthesis flows, and verification methodologies developed for binary logic require extension for multi-valued design. The limited tool support creates barriers to adoption and increases design effort for multi-valued systems.

Power and Performance Trade-offs

Multi-valued logic offers potential power reduction through decreased switching activity per bit of information transferred. With more information per signal transition, fewer transitions may be needed for equivalent computation.

However, the circuits that generate and detect multiple levels typically consume more power than binary equivalents. Static power from voltage dividers, increased sensing current for smaller margins, and more complex logic for level generation all contribute to overhead.

Performance benefits from reduced interconnect complexity may be offset by slower level transitions and more complex gate implementations. The net effect depends strongly on specific applications and implementation technologies.

High-Speed Communications

Serial communication links increasingly adopt multi-valued signaling to achieve higher data rates without proportionally increasing symbol rates. PAM-4 signaling in 100G Ethernet and beyond enables doubled data rates compared to binary signaling at the same symbol rate.

Channel bandwidth limitations make increasing symbol rates increasingly difficult, favoring multi-level signaling that packs more bits into each symbol. The additional receiver complexity for multi-level detection is acceptable when the alternative of higher symbol rates faces fundamental channel limitations.

Equalizer and signal processing complexity increases with multi-level signaling, but modern integrated circuit technology makes sophisticated signal processing practical. The trend toward higher-level signaling in communications is likely to continue as data rate demands grow.

High-Density Storage

Flash memory's success with multi-level cells demonstrates commercial viability of multi-valued storage. The density advantages outweigh the performance and endurance penalties for many consumer and enterprise applications.

Emerging memory technologies continue this trend, with research into multi-level operation for ReRAM, PCM, and other non-volatile memories. The potential for improved density without proportional cell size reduction motivates ongoing development.

DNA data storage, an emerging technology using synthetic DNA sequences for archival storage, inherently operates with four-valued signals corresponding to the four nucleotide bases. This natural quaternary representation provides extremely high storage density at the molecular level.

Specialized Computation

Certain computational problems map naturally to multi-valued representations. Fuzzy logic systems, which reason about degrees of truth rather than binary true/false, benefit from multi-valued hardware that directly represents intermediate truth values.

Pattern recognition and machine learning applications often involve analog or near-analog computation where multi-valued or truly analog processing can be more efficient than high-precision binary digital computation. The error tolerance of these applications accommodates the reduced precision of multi-valued systems.

Cryptographic applications have explored multi-valued logic for potential security benefits, though the relatively immature state of multi-valued implementation complicates security analysis.

The Setun Ternary Computer

The Setun, developed at Moscow State University under the leadership of Nikolai Brusentsov, became operational in 1958 as the first modern ternary computer. Using balanced ternary arithmetic with values {-1, 0, +1}, the Setun demonstrated practical advantages of ternary representation including simplified signed arithmetic.

Approximately 50 Setun computers were manufactured and deployed for scientific and educational use. The design's reliability and economy compared favorably with contemporary binary computers, validating balanced ternary as a practical computing approach.

Despite its success, the Setun did not lead to widespread ternary computing adoption. Binary computers benefited from larger research investment, more developed component supply chains, and increasing integration that amplified binary's manufacturing simplicity. The Setun remains an important demonstration that alternative number systems can work in practice.

Other Historical Implementations

Various other multi-valued computer projects explored alternatives to binary throughout computing history. The TERNAC, developed in the 1970s, implemented ternary computing with integrated circuits. Research projects at universities worldwide have produced ternary and quaternary processor implementations.

Multi-valued logic has seen more success in peripheral applications than in general-purpose computing. Memory systems, communication interfaces, and specialized accelerators have adopted multi-valued techniques where specific advantages outweigh the overhead of non-binary operation.

Emerging Technologies

New device technologies may prove more naturally suited to multi-valued operation than conventional CMOS. Memristive devices, with their inherently analog resistance states, could enable efficient multi-valued storage and computation. Quantum dots, carbon nanotubes, and other nanoscale devices offer possibilities for multi-valued operation at molecular scales.

Photonic computing using light intensity or wavelength for information encoding naturally supports multi-valued or even analog computation. The wavelength dimension provides a natural multi-valued representation distinct from binary electronic signaling.

Integration with Neural Computing

Neuromorphic computing, inspired by biological neural systems, increasingly embraces analog and multi-valued computation. Neural networks process information through weighted summation and thresholding, operations that map naturally to multi-valued and threshold logic implementations.

The convergence of multi-valued logic research with neural computing may produce hybrid architectures exploiting the strengths of both approaches. Multi-valued signals could represent neuron activation levels more efficiently than binary encoding, while threshold logic gates could implement neuron functions directly.

Standardization and Ecosystem Development

Broader adoption of multi-valued logic requires development of design tools, standard cells, and methodology comparable to what exists for binary design. Research into multi-valued logic synthesis, optimization, and verification continues, though gaps remain compared to mature binary tools.

Standard interfaces explicitly supporting multi-valued signaling, like PAM-4 for serial communications, enable incremental adoption without requiring wholesale conversion of existing systems. Similar standardization for memory interfaces and other critical functions could accelerate multi-valued logic deployment.