NULL Convention Logic Circuits Research Articles

A Scalable Formal Framework for the Verification and Vulnerability Analysis of Redundancy-Based Error-Resilient Null Convention Logic Asynchronous Circuits

The increasing demand for high-speed, energy-efficient, and miniaturized electronics has led to significant challenges and compromises in the domain of conventional clock-based digital designs, most notably reduced circuit reliability, particularly in mission-critical hardware. At scaled technology nodes, devices are vulnerable to transient or soft errors, such as Single Event Upset (SEU) and Single Event Latch-up (SEL). External radiation, internal electromagnetic interference (EMI), or noise are the primary sources of these errors, which can compromise the circuit functionality. In response to these challenges, the Quasi-Delay-Insensitive (QDI) Null Convention Logic (NCL) asynchronous design paradigm has emerged as a promising alternative, offering advantages such as ultra-low power performance, reduced noise and EMI, and resilience to process, voltage, and temperature variations. Moreover, its unique architecture and insensitivity to timing variations offers a degree of resistance against transient errors; however, it is not entirely resilient. Several resiliency schemes are available to detect and mitigate soft errors in QDI circuits, with approaches based on redundancy proving to be the most effective in ensuring complete resilience across all major QDI implementation paradigms, including NCL, Pre-charge/Weak-charge Half Buffers (PCHB/WCHB), and Sleep Convention Logic (SCL). This research focuses on one such redundancy-based resiliency scheme for QDI NCL circuits, known as the dual-modular redundancy-based NCL (DMR-NCL) architecture, and addresses the absence of formal methods for the verification and analysis of such circuits. A novel methodology has been proposed for formally verifying the correctness of DMR-NCL circuits synthesized from their synchronous counterparts, covering both safety (functional correctness) and liveness (the absence of deadlock). In addition, this research introduces a formal framework for the vulnerability analysis of DMR-NCL circuits against SEU/SEL. To demonstrate the framework’s efficacy and scalability, a prototype computer-aided support tool has been developed, which verifies and analyzes multiple DMR-NCL benchmark circuits of varying sizes and complexities.

THx2 Programmable Logic Block Architecture for Clockless Asynchronous FPGAs

To address some of the challenges of asynchronous design, we propose a new, decomposable asynchronous logic block architecture based on our TH<inline-formula> <tex-math notation="LaTeX">$x2$ </tex-math></inline-formula> programmable threshold cell, and we use it to implement common threshold functions found in asynchronous, null convention logic circuits. At a minimum, programmable gate arrays require a programmable logic cell that can implement a complete set of logic. It is well known that a NAND function forms a complete set of logic, and in null convention logic, the TH12 and TH22 threshold cells are used to form a basic two-input NAND function. The TH<inline-formula> <tex-math notation="LaTeX">$x2$ </tex-math></inline-formula> threshold cell is capable of performing both TH12 and TH22 operations, so it too forms a complete set of logic. In this paper, we present our eight-transistor mask-programmable gate array logic cell, 16-transistor field-programmable gate array logic cell, and new decomposable field-programmable gate array logic block architecture, all based on the TH<inline-formula> <tex-math notation="LaTeX">$x2$ </tex-math></inline-formula> threshold cell and suitable for implementing null convention logic asynchronous functions. To minimize the TH<inline-formula> <tex-math notation="LaTeX">$x2$ </tex-math></inline-formula> threshold cell area for both TH12 and TH22 modes, we designed a layout with common Euler paths and no diffusion breaks for both modes. The highly compact nature of the TH<inline-formula> <tex-math notation="LaTeX">$x2$ </tex-math></inline-formula> threshold cell&#x2013;along with the symmetry of the mask- and field-programmable gate array logic cells&#x2013;made it an ideal candidate for an asynchronous field-programmable logic block structure. This paper is part of an ongoing project, and it only addresses the programmable logic block architecture, not a complete FPGA fabric.

A dual-rail/single-rail hybrid system using null convention logic circuits

Null convention logic (NCL) is a good design approach for constructing a low-power and high-speed asynchronous system. However, NCL has a higher transistor count with a dual-rail structure, especially for large-scale circuits. To save NCL dual-rail overhead, we present an NCL dual-rail/single-rail hybrid system in which single-rail synchronous combinational logic is used between two NCL dual-rail registers. In addition, a 4-bit dual-rail/single-rail hybrid arithmetic logic unit (ALU) and a 4-bit dual-rail ALU are designed to compare performance. To achieve a faster speed, the operation logics in the hybrid ALU adopt transmission gates (TGs). Compared with the 4-bit NCL dual-rail ALU, the 4-bit hybrid ALU (OR operation) has advantages in smaller transistor count (reduced by 14.8%), smaller layout area (reduced by 0.16 mm2), lower power consumption (reduced by 47%), lower delay (reduced by 0.19 ns), and less effect of process/voltage/temperature (PVT) variations. Moreover, the 4-bit NCL dual-rail ALU is optimized with embedded registers in terms of transistor count (reduced by 4%), TASY (reduced by 0.18 ns), and power dissipation (reduced by 0.1 mW).

Transistor Count Reduction Technique for Clockfree Null-convention Arithmetic Logic Circuits

Null Convention Logic (NCL) is a robust clock-less technique for designing asynchronous delay-insensitive circuits. The traditional complementary metal oxide semiconductor (CMOS) approach is often used for designing NCL circuits, which tends to occupy a large area. To address this issue, a low power design technique Gate Diffusion Input (GDI) is introduced for designing the NCL circuits. This GDI design methodology is the promising alternative for the static CMOS designs, which allows the reduction in area and power consumption while maintaining the low complexity of the logic design. In this paper, a novel GDI based NCL designs are proposed and designed. However, the voltage swings in the GDI approach leads to the considerable amount of voltage drop at the output. This limitation is addressed by using low threshold transistors where a voltage drop is expected, and high threshold transistors are used for the regenerative inverters at the output. The proposed approach has been verified by designing the NCL Ripple Carry Adder (RCA), Unpipelined multiplier, pipelined multiplier and Unpipelined ALU by using the GDI technique. These models are designed and simulated using Cadence Virtuoso and an average of 13.5 % reduction in the transistor count is observed for these GDI based NCL models when compared to the CMOS models.

Novel Area-efficient Null Convention Logic based on CMOS and Gate Diffusion Input (GDI) Hybrid

Null convention logic (NCL) is a promising delay insensitive paradigm for constructing asynchronous circuits. Traditionally, NCL circuits are implemented utilizing complementary metal oxide semiconductor (CMOS) technology that has large area overhead. To address this issue, a HYBRID methodology is introduced for realizing NCL circuits in this paper. The proposed approach utilizes both CMOS and gate diffusion input (GDI) techniques to significantly reduce the area. Compared with the conventional static CMOS NCL counterpart, the HYBRID implementation of an NCL up counter demonstrate an average of 10% reduction in the transistor count.

Automated verification of input completeness for NCL circuits

An automated formal verification approach for ensuring input completeness of NULL Convention Logic (NCL) circuits is proposed. NCL circuits have the benefit that they can operate in extreme environments where traditional synchronous circuits fail due to significant fluctuations in circuit timing. Input completeness is a critical property to ensure correct functioning of NCL circuits in extreme environments and therefore is required to be verified. Note that an NCL circuit can be functionally correct and still not be input complete, which could cause the circuit to operate correctly under normal conditions, but malfunction only when the circuit timing is substantially changed (e.g. operating in a very hot or cold environment such as outer space).

Clock-Less DFT-Less Test Strategy for Null Convention Logic

Null Convention Logic (NCL) is a robust asynchronous technique that poses new challenges to test and testability strategies due to the lack of a clock signal and the state-holding behavior of the NCL gates. The lack of deterministic timing in NCL complicates the management of test timing, and stuck-at faults on gate internal feedback (GIF) of the NCL gates exhibit a totally different effect compared to that of stuck-at faults on the gate inputs. Stuck-at faults on gate internal feedback of NCL gates do not always cause an incorrect output and therefore are considered hard-to-detect or undetectable by automatic test pattern generation (ATPG) algorithms. Such faults could leave the primary outputs of the circuit completely unaffected or sometimes they only affect the circuit by early detection of completeness. This work first proposes a clock-less self-timed ATPG, with no added design for test (DFT), that detects all of the faults on the gate inputs and a share of those on the GIF of gates. Then, this work investigates the effectiveness of I_DDQ (quiescent current) test for detecting stuck-at faults on GIF of NCL gates. Hspice is used for implementing static and semi-static transistor-level NCL gates in (45 nm, 1.1 V) technology, for which the supply current is measured and compared for fault-free and faulty circuits. The experimental results show that the faulty current is orders of magnitude higher than the fault-free leakage current. This considerable difference shows that I_DDQ testing might be an efficient and low-cost candidate for detecting stuck-at faults on GIF of NCL gates. The proposed I_DDQ test method along with the self-timed ATPG has resulted in average 98.16 and 98.04 percent fault coverage for static and semi-static implementations of several NCL circuits, respectively. To the extent of our knowledge, this is the first work that has addressed clock-less, self-timed ATPG for NCL with no area overhead, and also the first work conducted on I_DDQ test for NCL.

Register-Less NULL Convention Logic

NULL Convention Logic (NCL) is a promising design paradigm for constructing low-power robust asynchronous circuits. The conventional NCL paradigm requires pipeline registers for separating two neighboring logic blocks, and those registers can account for up to 35% of the overall power consumption of the NCL circuit. This brief presents the Register-Less NCL (RL-NCL) design paradigm, which achieves low power consumption by eliminating pipeline registers, simplifying the control circuit, and supporting fine-grained power gating to mitigate the leakage power of sleeping logic blocks. Compared with the conventional NCL counterpart, the RL-NCL implementation of an 8-bit five-stage pipelined Kogge–Stone adder can reduce power dissipation by 56.4%–72.5% for the input data rate ranging from 10 to 900 MHz. Moreover, the RL-NCL implementation can reduce the transistor count of the adder by 49.5%.

Abstraction techniques to improve scalability of equivalence verification for NCL circuits

Asynchronous NULL convention logic (NCL) circuits are dual-rail quasi-delay-insensitive circuits that have many applications in high radiation and extreme temperature fluctuation environments such as space exploration. Two abstraction techniques are proposed that can be used to drastically improve the efficiency and scalability of formal equivalence verification targeted at NCL circuits. The effectiveness of the abstraction techniques have been demonstrated using a number of multiply and accumulate circuit benchmarks.

Gate Mapping Automation for Asynchronous NULL Convention Logic Circuits

Design automation techniques are a key challenge in the widespread application of timing-robust asynchronous circuit styles. In this paper, a new methodology for mapping multi-rail logic expressions to a NULL convention logic (NCL) gate library is proposed. The new methodology is then compared to another recently proposed mapping approach, demonstrating that the new methodology can further reduce the area and improve the delay of NCL circuits. Also, in contrast to the original approach, which only targets area reduction, the new methodology can target any arbitrary cost function or use any subset of the NCL gate library for mapping. In order to automate the new methodology and compare it with the original one, both methodologies were implemented in the Perl programming language and compared in terms of mapping performance and runtime. The results show that, depending on the test circuit, the new methodology can offer up to 10% improvement in area, and 39% improvement in delay.

Designing Asynchronous Circuits using NULL Convention Logic (NCL)

Designing Asynchronous Circuits using NULL Convention Logic (NCL) begins with an introduction to asynchronous (clockless) logic in general, and then focuses on delay-insensitive asynchronous logic design using the NCL paradigm. The book details design of input-complete and observable dual-rail and quad-rail combinational circuits, and then discusses implementation of sequential circuits, which require datapath feedback. Next, throughput optimization techniques are presented, including pipelining, embedding registration, early completion, and NULL cycle reduction. Subsequently, low-power design techniques, such as wavefront steering and Multi-Threshold CMOS (MTCMOS) for NCL, are discussed. The book culminates with a comprehensive design example of an optimized Greatest Common Divisor circuit. Readers should have prior knowledge of basic logic design concepts, such as Boolean algebra and Karnaugh maps. After studying this book, readers should have a good understanding of the differences between asynchronous and synchronous circuits, and should be able to design arbitrary NCL circuits, optimized for area, throughput, and power. Table of Contents: Introduction to Asynchronous Logic / Overview of NULL Convention Logic (NCL) / Combinational NCL Circuit Design / Sequential NCL Circuit Design / NCL Throughput Optimization / Low-Power NCL Design / Comprehensive NCL Design Example

Design of an FPGA Logic Element for Implementing Asynchronous NULL Convention Logic Circuits

Two versions of a reconfigurable logic element are developed for use in constructing afield-programmable gate array NULL convention logic (NCL) field-programmable gate array (FPGA): one with extra embedded registration capability, which requires additional area, and one without. Both versions can be configured as any of the 27 fundamental NCL gates, including resettable and inverting variations, and both can utilize embedded registration for gates with three or fewer inputs; however, only the version with the additional embedded registration capability can utilize embedded registration with four-input gates. These two approaches are compared with each other and with an existing approach, showing that both versions developed herein yield a more area efficient NCL circuit implementation, compared to the previous work. The two FPGA logic elements are simulated at the transistor level using the 1.8-V, 180-nm TSMC CMOS process.

Cycle decomposition in NCL

In null convention logic (NCL) circuits, cycles are the fundamental unit of data storage, roughly equivalent to combinational logic bounded by latches in clocked design. Implementing the various tools common to IC design flows, such as static timing analysis and scan insertion, requires accurately identifying these cycles. Threshold gates are the basic building blocks of NCL cycles. To date, mechanisms for automatically identifying relevant NCL circuit cycles have been lacking. The NCL analyzer solves the problem of automatically identifying cycles from a gate-level netlist. It does this by identifying the acknowledge signal feeding a register from its relative signal polarity and then finding the intersection of a forward and reverse circuit traversal. Although the NCL analyzer is currently a stand-alone tool, we expect it will become an integral part of nearly all NCL-specific tools - including static timing analysis, orphan checking, ATPG, and possibly synthesis.