Circuit testable design and universal test sets for multiple-valued logic functions

The circuit testable realizations of multiple-valued functions are studied in this letter. First of all, it is shown that one vector detects all skew faults in multiplication modulo circuits or in addition modulo circuits, and n＋1 vectors detect all skew faults in the circuit realization of multiplevalued functions with n inputs. Secondly, min（max） bridging fault test sets with n＋2 vectors are presented for the circuit realizations of multiple-valued logic functions. Finally, a tree structure is used instead of cascade structure to reduce the delay in the circuit realization, it is shown that three vectors are sufficient to detect all single stuck-at faults in the tree structure realization of multiplevalued logic functions.     

FAULT DETECTION TEST SET FOR TESTABLE REALIZATIONS OF LOGIC FUNCTIONS WITH ESOP EXPRESSIONS

The circuit testable realization and its fault detection for logic functions with ESOP （EXOR-Sum-Of-Products） expressions are studied. First of all, for the testable realization by using XOR gate cascade, a test set with 2n ＋ m ＋ 1 vectors for the detections of AND bridging faults and a test set with 2n ＋ m vectors for the detections of OR bridging faults are presented. Secondly, for the testable realization by using ）（OR gate tree, a test set with 2n ＋ m vectors for the detections of AND bridging faults and a test set with 3n ＋ m ＋ 1 vectors for the detections of OR bridging faults are presented. Finally, a single fault test set with n ＋ 5 vectors for the XOR gate tree realization is presented. Where n is the number of input variables and m is the number of product terms in a logic function.     

Robust tests for parity trees

Linear logic circuits are used extensively in digital computing and signal processing systems. They are constructed as regular arrays (for example as cascade or tree circuits), employing linear gates such as Exclusive OR (EOR) and Exclusive NOR (ENOR) gates. Earlier studies on fault diagnosis in linear logic circuits were based on the classical fault model of line stuck-at faults. Transistor stuck-open (SOP) and stuck-on (SON) faults in linear circuits were studied recently, but the effect of signal transients due to circuit delays and time skews in input changes were not considered in the derivation of test sequences. These latter factors are known to cause invalidation of two pattern tests for stuck-open faults. In this article we consider the problem of generating robust tests for linear logic circuits. These tests are not affected by circuit transients caused by delays. A major finding in this paper is that, if the test invalidation problem is redressed by introducing robust tests, the test length becomes a linear function of the depth of the circuit as opposed to the constant number of tests derived in previous studies, by neglecting circuit transients. A lower bound on minimum number of distinct test patterns needed for a tree of EOR gates of depthd is derived. This number depends on the specific implementation of the gate. Robust test-generation procedures are proposed for both single and multiple fault models and their optimalities are argued. Given that every gate in a parity tree is robustly testable, a test sequence that can test for all faults in the circuit, regardless of the nature of gate implementation, is calleduniversal robust test sequence for a parity tree. Finally we propose an optimal universal robust test sequence.     

Synthesis method for testable electrical networks using 1st order building blocks

This work presents a method for synthesizing testable continuous-time linear time-invariant electrical networks using 1st order blocks for the implementation of analog linear circuits. A functional-structural fault model for the block, and a fault dictionary are proposed together with a simple set of test vectors. The method allows, also, the fault grade evaluation for the modeled faults. The results obtained from the two application examples have shown the suitability of the approach as a design for test method for analog circuits.     

基于故障映射的并行故障仿真方法

提出了基于故障映射的4值并行故障仿真方法.这一方法首先把电路划分成无扇出区域和扇出茎区域,然后将非扇出茎故障映射为扇出茎故障,减少了需要显式并行仿真的故障数目,提高了仿真器的性能.实验结果验证了文中方法的有效性.     

Testability Properties of Divergent Trees

The testability of a class of regular circuits calleddivergent trees is investigated under a functional fault model. Divergent trees include such practical circuits as decoders anddemultiplexers. We prove that uncontrolled divergent trees aretestable with a fixed number of test patterns (C-testable) if andonly if the module function is surjective. Testable controlled treesare also surjective but require sensitizing vectors for errorpropagation. We derive the conditions for testing controlleddivergent trees with a test set whose size is proportional to thenumber of levels p found in the tree (L-testability). By viewing a tree as overlapping arrays of various types, we also deriveconditions for a controlled divergent tree to be C-testable. Typicaldecoders/demultiplexers are shown to only partially satisfy L- andC-testability conditions but a design modification that ensuresL-testability is demonstrated.     

基于Radix-4 Booth编码的模2n+1乘法器设计

模2n+1乘法(n=8、16)在分组密码算法中比较常见,如IDEA算法,但由于其实现逻辑复杂,往往被视为密码算法性能的瓶颈。提出了一种适用于分组密码算法运算特点的基于Radix-4 Booth编码的模2n+1乘法器实现方法,其输入/输出均无需额外的转换电路,并通过简化部分积生成、采用重新定义的3-2和4-2压缩器等措施以减少路径时延和硬件复杂度。比较其他同类设计,该方法具有较小的面积、时延,可有效提高分组密码算法的加解密性能。     

An efficient tree architecture for modulo 2 n +1 multiplication

Modulo 2 ⁿ +1 multiplication plays an important role in the Fermat number transform and residue number systems; the diminished-1 representation of numbers has been found most suitable for representing the elements of the rings. Existing algorithms for modulo (2 ⁿ +1) multiplication either use recursive modulo (2 ⁿ +1) addition, or a regular binary multiplication integrated with the modulo reduction operation. Although most often adopted for largen, this latter approach requires conversions between the diminished-1 and binary representations. In this paper we propose a parallel fine-grained architecture, based on a Wallace tree, for modulo (2 ⁿ +1) multiplication which does not require any conversions; the use of a Wallace tree considerably improves the speed of the multiplier. This new architecture exhibits an extremely modular structure with associated VLSI implementation advantages. The critical path delay and the hardware requirements of the new multiplier are similar to that of a correspondingn×n bit binary multiplier.     

通用Toffoli可逆门的固定故障测试

可逆电路技术在低功耗芯片和量子通信中广泛使用。目前,大部分学者着重研究可逆电路的合成,对电路的故障测试却很少问津,但是可逆电路的测试在应用中却十分重要。文中构造了一种四输入通用Toffoli门（universal toffoli gate,UTG）用来检测电路故障,这个门可以实现所有基本的布尔逻辑。UTG门可以检测到所...     

An efficient tree architecture for modulo 2n+1 multiplication

Modulo 2 ⁿ +1 multiplication plays an important role in the Fermat number transform and residue number systems; the diminished-1 representation of numbers has been found most suitable for representing the elements of the rings. Existing algorithms for modulo (2 ⁿ +1) multiplication either use recursive modulo (2 ⁿ +1) addition, or a regular binary multiplication integrated with the modulo reduction operation. Although most often adopted for largen, this latter approach requires conversions between the diminished-1 and binary representations. In this paper we propose a parallel fine-grained architecture, based on a Wallace tree, for modulo (2 ⁿ +1) multiplication which does not require any conversions; the use of a Wallace tree considerably improves the speed of the multiplier. This new architecture exhibits an extremely modular structure with associated VLSI implementation advantages. The critical path delay and the hardware requirements of the new multiplier are similar to that of a correspondingn×n bit binary multiplier.     

Test Set and Fault Partitioning Techniques for Static Test Sequence Compaction for Sequential Circuits

We propose a new static test set compaction method based on a careful examination of attributes of fault coverage curves. Our method is based on two key ideas: (1) fault-list and test-set partitioning, and (2) vector re-ordering. Typically, the first few vectors of a test set detect a large number of faults. The remaining vectors usually constitute a large fraction of the test set, but these vectors are included to detect relatively few hard faults. We show that significant compaction can still be achieved by partitioning faults into hard and easy faults, and compaction is performed only for the hard faults. This significantly reduces the computational cost for static test set compaction without affecting quality of compaction. The second key idea re-orders vectors in a test set by moving sequences that detect hard faults to the beginning of the test set. Fault simulation of the newly concatenated re-ordered test set results in the omission of several vectors so that the compact test set is smaller than the original test set. Experiments on several ISCAS 89 sequential benchmark circuits and large production circuits show that our compaction procedure yields significant test set reductions in low execution times.     

State and Fault Information for Compaction-Based Test Generation

We present a new test generation procedure for sequential circuits using newly traversed state and newly detected fault information obtained between successive iterations of vector compaction. Two types of techniques are considered. One is based on the new states a sequential circuit is driven into, and the other is based on the new faults that are detected between consecutive iterations of vector compaction. These data modify an otherwise random selection of vectors, to bias vector sequences that cause the circuit to reach new states, and cause previously undetected faults to be detected. The biased vectors, when used to extend the compacted test set, provide a more intelligent selection of vectors. The extended test set is then compacted. Repeated applications of state and fault analysis, vector generation and compaction produce significantly high fault coverage using relatively small computing resources. We obtained improvements in terms of higher fault coverage, fewer vectors for the same coverage, or smaller number of iterations and time required, consistently for several benchmark circuits.     

An efficient and high-speed VLSI implementation of optimal normal basis multiplication over GF(2m)

Finite field multiplication is one of the most important operations in the finite field arithmetic and the main and determining building block in terms of overall speed and area in public key cryptosystems. In this work, an efficient and high-speed VLSI implementation of the bit-serial, digit-serial and bit-parallel optimal normal basis multipliers with parallel-input serial-output (PISO) and parallel-input parallel-output (PIPO) structures are presented. Two general multipliers, namely, Massey–Omura (MO) and Reyhani Masoleh–Hassan (RMH) are considered as case study for implementation. These multipliers are constructed by using AND, XOR–AND and XOR tree components. In the MO multiplier, to have strong input signals and have a better implementation, the row of AND gates are implemented by using inverter and NOR components. Also the XOR–AND component in the RMH structure is implemented using a new low-cost structure. The XOR tree in both multipliers consists of a high number of logic stages and many inputs; therefore, to optimally decrease the delay and increase the drive ability of the circuit for different loads, the logical effort method is employed as an efficient method for sizing the transistors. The multipliers are first designed for different load capacitances using different structures and different number of stages. Then using the logical effort method and a new proposed 4-input XOR gate structure, the circuits are modified for acquiring minimum delay. Using 0.18 μm CMOS technology, the bit-serial, digit-serial and bit-parallel structures with type-1 and type-2 optimal normal basis are implemented over the finite fields GF(2²²⁶) and GF(2²³³) respectively. The results show that the proposed structures have better delay and area characteristics compared to previous designs.     

Bounds on the sizes of irredundant test sets and sequences for combinational logic networks

We present a method of determining lower and upper bounds on the number of tests required to detect all detectable faults in combinational logic networks. The networks are composed of AND, OR, NAND, NOR, and XOR gates. The fault model assumes that single stuck-at-zero faults occur on the lines of the networks, with the additional requirement that XOR gates be tested with all possible input combinations. The goal is to provide a simple and efficient implementation that processes the fanout-free subnetworks separately, and then combines the results without the need to consider the effects of reconvergent fanout. We introduce the concepts of irredundant test sets, where no test can be deleted regardless of the order of test application, and irredundant test sequences, where every test detects at least one additional fault when tests are applied in order. Identifying and differentiating between these types of collections of tests allows us to understand more precisely the mechanisms and expected performance of test generation and test compaction methods. We apply our test counting technique and two other published procedures to a set of benchmark circuits. Our bounds are shown to compare favorably to the results obtained by the other published approaches. We obtain minimal and maximal test sets and test sequences using a greedy optimization technique. Our bounds are shown to produce tight bounds for the smaller circuits; they grow more conservative as the size of the circuits increase.     

Self-Testing Embedded Two-Rail Checkers

This paper presents a new simple and straightforward method for designing Completely Testable Embedded (CTE) parity trees, and Self-Testing Embedded (STE) two-rail checkers. In the design of CTE parity trees the two inputs XOR gate has been used as the building block. In the case of STE two-rail checkers with n input pairs the building block is the two-rail checker with 2 input pairs. During normal, fault free, operation each XOR gate receives all possible input vectors, while each two-rail checker with 2 input pairs receives all possible code input vectors. The great advantage of the proposed method is that it is the only one that gives in a simple and straightforward way an optimal CTE/STE tree realization with respect to the hardware (number of blocks) and the speed (number of block levels). Designing the two input two-rail checker as proposed by Lo in IEEE J. of Solid-State Circuits, 1993, we get optimal STE two-rail checkers taking into account realistic faults.     

Scan power-aware deterministic test scheme using a low-transition linear decompressor

Growing test data volume and excessive testing power are both serious challenges in the testing of very large-scale integrated circuits. This article presents a scan power-aware deterministic test method based on a new linear decompressor which is composed of a traditional linear decompressor, k-input AND gates and T flip-flops. This decompression architecture can generate the low-transition deterministic test set for a circuit under test. When applying the test patterns generated by the linear decompressor, only a few transitions occur in the scan chains, and hence the switching activity during testing decreases significantly. Entire test flow compatible with the design is also presented. Experimental results on several large International Symposium on Circuits and Systems’89 and International Test Conference’99 benchmark circuits demonstrate that the proposed methodology can reduce test power significantly while providing a high compression ratio with limited hardware overhead.     

Modified Low-Complexity Chase Soft-Decision Decoder of Reed–Solomon Codes

Silicon-on-Insulator CMOS fabrication technologies are now available that offer a number of unique advantages including the availability of multiple simultaneous transistor thresholds. This paper proposes and analyzes a number of circuits for a reconfigurable array organization based on a balanced ternary logic system in which the logic set {− 1, 0, + 1} maps directly to equivalent voltage levels {−1V, 0V, +1V}. A number of low-power, high-speed components, such as a ternary buffer, flip-flop and look-up table, are described and simulated based on the characteristics of a commercially available silicon-on-sapphire process. A brief analysis indicates that the circuits will be capable of operating at the 22 nm technology node and beyond. A simple example of a Sigma-Delta Modulated FIR filter is mapped to the array and some preliminary estimates are made of its performance and area based on both 3-input and 4-input look-up tables. The simulated ternary array is shown to be capable of operating at clock speeds of more than 200 MHz such that it will readily support standard video bandwidths at useful over-sampling ratios.     

An Exact approach for Complete Test Set Generation of Toffoli-Fredkin-Peres based Reversible Circuits

Reversible logic has gained interest of researchers worldwide for its ultra-low power and high speed computing abilities in the future quantum information processing. Testing of these circuits is important for ensuring high reliability of their operation. In this work, we propose an ATPG algorithm for reversible circuits using an exact approach to generate CTS (Complete Test Set) which can detect single stuck-at faults, multiple stuck-at faults, repeated gate fault, partial and complete missing gate faults which are very useful logical fault models for reversible logic to model any physical defect. Proposed algorithm can be used to test a reversible circuit designed with k-CNOT, Peres and Fredkin gates. Through extensive experiments, we have validated our proposed algorithm for several benchmark circuits and other circuits with family of reversible gates. This algorithm produces a minimal and complete test set while reducing test generation time as compared to existing state-of-the-art algorithms. A testing tool is developed satisfying the purpose of generating all possible CTS’s indicating the simulation time, number of levels and gates in the circuit. This paper also contributes to the detection and removal of redundant faults for optimal test set generation.     

Physical design of testable VLSI: techniques and experiments

It is shown that the layout of VLSI circuits can affect testability and in some cases reduce the number of faults likely in a design, easing test generation. A method for analyzing circuits at the symbolic layout level and enhancing testability using local transformations is presented. To demonstrate the application of the technique a set of CMOS standard cells was redesigned. The standard cells are used in the MIS synthesis system, allowing the designer to modify interactively designs to perform tradeoff analysis on testable designs. To show the usefulness of the technique, an experiment was performed: example circuits were synthesized, and test vectors were generated and then used in a transistor-level fault simulator. It was found that the modified designs have significantly higher fault coverage than unmodified designs. A strategy for the synthesis of easily testable combinational random logic circuits is presented     

A New Test Point Selection Method for Analog Continuous Parameter Fault

Discrete hard fault is always tested in existing node selection methods for analog circuit diagnosis. Actually, analog component parameter changes continuously and output node voltages distribute in a continuous voltage interval. In this paper, an novel test node selection method is proposed for continuous parameter shifting (CPS) fault. Firstly, CPS faults are sampled by parameter scan simulation in a single test frequency. Collected node voltages are seen as a data set in a statistical distribution. Secondly, ambiguous faults are identified according to the independent distributions of all CPS faults. The independence of CPS fault sample is deduced by Kruskal-Wallis non-parametric testing. Then, new fault dictionaries are generated for each test node according to ambiguous interval. The proposed fault dictionary represents the mutual independence of each pair of CPS faults. Finally, as fault dictionaries are considered as connected graphs, the optimal test nodes are selected based on an improved depth first search (DFS) algorithm. The effectiveness of method is verified by testing linear and nonlinear circuits.