Simplifying the Boolean Equation Based on Simulation System using Karnaugh Mapping Tool in Digital Circuit Design

In computerized integrated circuits, the fundamental principle intends to avoid the multifaceted nature of the circuitry by making it as brief as attainable and minimize the expenditure. Techniques like Quine- McCluskey (QM) and Karnaugh Map (K-Map) are often used approaches of simplifying Boolean functions. This study presents a recreation framework of simplification of the Boolean capacities by the utilize of the K- Map definition for beginner-level learners. It uses the algebraic expression of the Boolean function to decrease the number of terms, generates a circuit, and does not use any redundant sets. In this way, it gets to be competent to deal with lots of parameters and minimize the computational cost. The result of the assessment is performed in this paper by contrasting it with the C- Minimizer algorithm. In computation time terms, the result appears that our comprehensive K mapping tool outflanks in current procedures, and the relative error accomplishes a lower rate of percentage (2%), which fulfills the satisfactory level. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 76-84

A Novel Bottom-Up/Top-Down Hybrid Strategy-Based Fast Sequential Fault Diagnosis Method

Sequential fault diagnosis is a kind of important fault diagnosis method for large scale complex systems, and generating an excellent fault diagnosis strategy is critical to ensuring the performance of sequential diagnosis. However, with the system complexity increasing, the complexity of fault diagnosis tree increases sharply, which makes it extremely difficult to generate an optimal diagnosis strategy. Especially, because the existing methods need massive redundancy iteration and repeated calculation for the state parameters of nodes, the resulting diagnosis strategy is often inefficient. To address this issue, a novel fast sequential fault diagnosis method is proposed. In this method, we present a new bottom-up search idea based on Karnaugh map, SVM and simulated annealing algorithm. It combines failure sources to generate states and a Karnaugh map is used to judge the logic of every state. Eigenvalues of SVM are obtained quickly through the simulated annealing algorithm, then SVM is used to eliminate the less useful state. At the same time, the bottom-up method and cost heuristic algorithms are combined to generate the optimal decision tree. The experiments show that the calculation time of the method is shorter than the time of previous algorithms, and a smaller test cost can be obtained when the number of samples is sufficient.

Research on a design method of pneumatic logic control system

Aiming at the complex characteristics of the sequential logic control system design, such as X-D diagram and karnaugh map method, a design method based on stepper module was proposed, the procedure of which does not need to be checked and corrected. The design of different pneumatic circuits was carried out with the automatic drilling machine as the application object. First, a stepper module composed of a two-position three-way valve and a dual-pressure valve was constructed, and its structure principle was analyzed in detail. Next, three kinds of stroke programs were listed by analyzing the working process of automatic drilling machine, which were multi-cylinder single reciprocating, multi-cylinder multi reciprocating and multi-cylinder multi-section reciprocating stroke program, and the pneumatic circuit control system was designed by the stepper module method. Finally, the pneumatic circuit was simulated and analyzed using the software Fluid-SIM. The simulation results showed that each actuator can complete the corresponding actions according to the design requirements, which verified the correctness and reliability of the stepper module design method. This work would provide a fast and effective method for the design of the sequential logic control system.

Utilization of the Karnaugh Map in Exploring Cause-effect Relations Modeled by Partially-defined Boolean Functions

This paper utilizes a modern regular and modular eight-variable Karnaugh map in a systematic investigation of cause-effect relationships modeled by partially-defined Boolean functions (PDBF) (known also as incompletely specified switching functions). First, we present a Karnaugh-map test that can decide whether a certain variable must be included in a set of supporting variables of the function, and, otherwise, might enforce the exclusion of this variable from such a set. This exclusion is attained via certain don’t-care assignments that ensure the equivalence of the Boolean quotient w.r.t. the variable, and that w.r.t. its complement, i.e., the exact matching of the half map representing the internal region of the variable, and the remaining half map representing the external region of the variable, in which case any of these two half maps replaces the original full map as a representation of the function. Such a variable exclusion might be continued w.r.t. other variables till a minimal set of supporting variables is reached. The paper addresses a dominantly-unspecified PDBF to obtain all its minimal sets of supporting variables without resort to integer programming techniques. For each of the minimal sets obtained, standard map methods for extracting prime implicants allow the construction of all irredundant disjunctive forms (IDFs). According to this scheme of first identifying a minimal set of supporting variables, we avoid the task of drawing prime-implicant loops on the initial eight-variable map, and postpone this task till the map is dramatically reduced in size. The procedure outlined herein has important ramifications for the newly-established discipline of Qualitative Comparative Analysis (QCA). These ramifications are not expected to be welcomed by the QCA community, since they clearly indicate that the too-often strong results claimed by QCA adherents need to be checked and scrutinized.

Using Eight-Variable Karnaugh Maps to Unravel Hidden Technicalities in Qualitative Comparative Analysis

We use a regular and modular eight-variable Karnaugh map to reveal some technical details of Boolean minimization usually employed in solving problems of Qualitative Comparative Analysis (QCA). We utilize as a large running example a prominent eight-variable political-science problem of sparse diversity (involving a partially-defined Boolean function (PDBF), that is dominantly unspecified). We recover the published solution of this problem, showing that it is merely one candidate solution among a set of many equally-likely competitive solutions. We immediately obtain one of these rival solutions, that looks better than the published solution in two aspects, namely: (a) it is based on a smaller minimal set of supporting variables, and (b) it provides a more compact Boolean formula. However, we refrain from labelling our solution as a better one, but instead we stress that it is simply un-comparable with the published solution. The comparison between any two rival solutions should be context-specific and not tool-specific. In fact, the Boolean minimization technique, borrowed from the area of digital design, cannot be used as is in QCA context. A more suitable paradigm for QCA problems is to identify all minimal sets of supporting variables (possibly via integer programming), and then obtain all irredundant disjunctive forms (IDFs) for each of these sets. Such a paradigm stresses inherent ambiguity, and does not seem appealing as the QCA one, which usually provides a decisive answer (irrespective of whether it is justified or not).The problem studied herein is shown to have at least four distinct minimal sets of supporting variables with various cardinalities. Each of the corresponding functions does not have any non-essential prime implicants, and hence each enjoys the desirable feature of having a single IDF that is both a unique minimal sum and the complete sum. Moreover, each of them is unate as it is expressible in terms of un-complemented literals only. Political scientists are invited to investigate the meanings of the (so far) abstract formulas we obtained, and to devise some context-specific tool to assess and compare them.

Utilization of Eight-Variable Karnaugh Maps in the Exploration of Problems of Qualitative Comparative Analysis

Qualitative Comparative Analysis (QCA) is an emergent methodology of diverse applications in many disciplines. However, its premises and techniques are continuously subject to discussion, debate, and (even) dispute. We use a regular and modular Karnaugh map to explore a prominent recently-posed eight-variable QCA problem. This problem involves a partially-defined Boolean function (PDBF), that is dominantly unspecified. Without using the algorithmic integer-programming approach, we devise a simple heuristic map procedure to discover minimal sets of supporting variables. The eight-variable problem studied herein is shown to have at least two distinct such sets, with cardinalities of 4 and 3, respectively. For these two sets, the pertinent function is still a partially-defined Boolean function (PDBF), equivalent to 210 = 1024 completely-specified Boolean functions (CSBFs) in the first case, and to four CSBFs only in the second case. We obtained formulas for the four functions of the second case, and a formula for a sample fifth function in the first case. Although only this fifth function is unate, each of the five functions studied does not have any non-essential prime implicant, and hence each of them enjoys the desirable feature of having a single IDF that is both a unique minimal sum and the complete sum. According to our scheme of first identifying a minimal set of supporting variables, we avoided the task of drawing prime-implicant loops on the initial eight-variable map, and postponed this task till the map became dramatically reduced in size. Our map techniques and results are hopefully of significant utility in future QCA applications.

Penggunaan Aplikasi Karnaugh Map (K-Map) Solver dalam Kursus Sistem Elektronik Digital

Aplikasi Karnaugh Map (K-Map) Solver telah dilaksanakan dalam kursus Sistem Elektronik Digital sebagai bahan bantu mengajar proses pengajaran dan pembelajaran operasi Boolean. Karnaugh Map merupakan teknik mudah untuk meringkaskan atau memudahkan persamaan operasi Boolean melalui cara pemetaan. Aplikasi ini adalah mesra pengguna dimana ia dapat menghasilkan keluaran persamaan yang ringkas melalui pemetaan Karnaugh Map. Aplikasi ini sangat mudah digunakan kerana mempunyai jadual kebenaran serta dilengkapi litar logik bagi persamaan yang telah diringkaskan. Perisian aplikasi ini juga dijadikan sebagai panduan kepada pelajar serta pensyarah untuk lebih memahami pemetaan Karnaugh Map. Kelebihan aplikasi ini adalah meringkaskan persamaan Boolean dengan lebih tepat, cepat. mudah difahami dan menjimatkan masa. Tujuan penggunaan aplikasi ini adalah untuk meningkatkan pemahaman pelajar terhadap operasi Boolean menggunakan Karnaugh Map. Keberkesanan aplikasi ini dapat dikenalpasti melalui soal selidik dan keputusan laporan Course Outcome Review Report (CORR) dari sistem SPMP. Hasil dapatan soal selidik dan laporan CORR mendapati prestasi pembelajaran pelajar selepas menggunakan aplikasi ini meningkat. Kesimpulannya aplikasi ini dapat meningkatkan kefahaman dan menarik minat pelajar disamping mengaplikasikan kemahiran teknologi dalam pengajaran dan pembelajaran.

Reliability Evaluation of Rooftop Solar Photovoltaics Using Coherent Threshold Systems

The trend for use of rooftop solar photovoltaics (PV) is rising due to their promising economic potential as a source of clean renewable energy. In general, a source of renewable solar energy consists of solar PV, an automatic charge controller, a battery pack, and an inverter. The reliability of a rooftop solar PV system is evaluated herein as that of a coherent threshold system (CTS). First, we utilize the unit-gap method and the fair-power method to verify that a given Boolean function is a threshold one and to identify its threshold and component weights. Both methods utilize specific features of the Karnaugh map (K-map). The unit-gap method uses the map to list all necessary inequalities by inspection, and then reduce them significantly by omitting dominated ones. The fair-power method uses the Karnaugh map to compute Banzhaf indices by appropriate map folding followed by XORing of true cells and false cells. We evaluate the CTS reliability via a recursive algorithm based on the Boole-Shannon’s expansion in the switching domain, which is transformed via the real transform to the total probability law in the probability domain.