File Name: a symbolic analysis of relay and switching circuits .zip
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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: In the control and protective circuits of complex electrical systems it is frequently necessary to make intricate interconnections of relay contacts and switches. Examples of these circuits occur in automatic telephone exchanges, industrial motor-control equipment, and in almost any circuits designed to perform complex operations automatically.
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Switching circuits that were originally proposed by Shannon in and nowadays widely used in telecommunication represent an alternative and efficient means to realize fast-speed and high-bandwidth communication. Using a routing strategy on a programmable DNA switch canvas, we show that arbitrary Boolean functions can be represented by DSCs and implemented with molecular switches with high computing speed.
We expect that DSCs provide a design paradigm for digital computation with biomolecules. DNA strand displacement reactions SDRs 1 , 2 , 3 have been employed to implement highly complex tasks such as molecular computing 4 , 5 , information processing 6 , 7 , 8 , and nanorobots 9 , 10 , In molecular computing, molecular circuits operate by the action of orthogonal molecules Hence, when the orthogonality decreases with circuit scale 13 , the actual achievable size is restricted, which is different with electronic circuits in which all elements are driven by the same electric signal.
SDR enables an enzyme-free implementation strategy to develop molecular circuits for arithmetical purpose 14 , 15 , which offers high selection space of orthogonal molecules Recent advances in modular molecular design and programmable reaction dynamics have led to the development of SDR-based Boolean logic gates with unparalleled complexity 5 , 13 , 17 , 18 , However, limitations associated with logic gate circuits emerges, which hinders the scale-up for practical achievable computational tasks as follows.
However, the thresholding and amplifying process generally poses a limit on the computing speed 5. As the NOT gate started produce ON signals before receiving the output of its upstream gate, the circuit might generate a false output.
During the early stage of electronic circuits, Shannon 27 established a systematic symbolic approach to design relay contacts or switching circuits SCs. In theory, any digital circuit can be represented by a set of equations, the terms of the equations corresponding to certain switches in the circuits. SCs can implement arbitrary digital functions in an efficient and economical manner.
For example, SCs form the basis of modern telecommunication that is characteristic of fast speed and high bandwidth. In a typical DSC, switches act as the sole basic functional element in a circuit, the molecular design is thus uniform, which allows high modularity, programmability, and scalability.
The direction of current signal transmission can be finely controlled by the difference in the free energy of molecules in the reaction pathway.
We also expect the increase of the computing speed with the reduced use of orthogonal molecules. A typical electronic SC consists of switches that connects or disconnects two nodes depending on the input voltage In this design, a DSC contains up to three types of molecular elements.
A starting switch at the entrance of the circuit responds to its switching signal and generates a current signal. A downstream switch responds to the current signal and switching signal, producing a current signal. Finally, a reporter responds to the current signal and generates fluorescent output. The response to a switching signal is realized with a molecular switch as shown in Fig. Molecular implementation of the switch function is realized by toehold-mediated SDR.
The released current signal is transmitted to a downstream switch to activate the responsive function of the downstream switch Fig. We designed the downstream switch molecule with two binding domains: C domain to respond to a current signal and S domain to respond to a switching signal.
The switch cannot flip to the ON state in the absence of the current signal. The transmission of the current signal from an upstream switch to a downstream switch is achieved by the hybridization of the current signal with the downstream switch through C domain, exposing the toehold for the binding of switching signal.
Typically, a DSC contains three types of elementary molecules: 1 Starting switch that responds to its switching signal. Boolean functions were realized with DSCs by programming the connection topologies of molecular switches.
Switching signals acted as inputs for Boolean computation. The AND logic was implemented with two switches in series Fig. Two switches in parallel performed OR logic Fig. This function was realized with a DSC with only three switches Fig. We first experimentally tested the switching and signal transmission functions using a one-switch circuit and a circuit with two series switches, respectively. The signal transmission process in the series circuit is shown in Fig.
The circuit contained an upstream switch x and a downstream switch y. Initially, switch x was OFF and switch y was blocked as the current signal had not arrived. Switching signal x flipped switch x to the ON state and released a current signal.
The current signal was then transmitted to switch y, allowing switch y to respond to its switching signal. The current signal generated by switch y was read out by a reporter. Corresponding SDRs are illustrated in Fig. Single-stranded x representing a switching signal bound to switch S x , displaced the current signal strand and released it.
As a result, switch x jumped from OFF to ON state fully double-stranded , generating a current signal. The molecule acting as a downstream switch y was named CS y with a C domain in addition to the S domain. Current signal from switch x interacted with CS y and switch y was activated by exposing the middle toehold. Then, switching signal y bound to switch y via the exposed toehold, generating a current signal.
Finally, the reporter molecule converted molecular concentration of the current molecule from switch y to fluorescence intensity using a fluorophore-quencher pair. Source data are provided as a Source Data file. The one-switch circuit was tested with and without the addition of switching signal and it gave the correct outputs.
In the experiments, all the circuit components, except the switching signal strand, were mixed on ice according to the optimized molar ratio of components in TE buffer with These results suggested that the DNA switch responded effectively to its switching signal. For the circuit with two series switches, upstream switch x was at 1. These two concentrations were used to ensure that the upstream switch could produce sufficient output for the downstream switch Supplementary Fig.
The essential strategy was that the concentration of a switch was determined such that this switch could always generate sufficient output strands for its downstream switches. This strategy for determination of concentrations in cascade was applied to all circuits.
These results are consistent with the designed function of series switches, with a computing speed much faster than reactions using logic gates in solution several hours 1 , 4 , With the programmability of C domain on downstream switch molecules, the current signal from an upstream switch can be easily transmitted to multiple downstream switches fan-out. We designed and tested a DSC with a two-output switch Fig. As shown in Fig. Current signal from S w interacted with both C domains that blocked switch x and y, resulting in activation of the two switches.
To overcome signal decay, concentration ratio of upstream and downstream was optimized Supplementary Fig. With the programmability of current signal strand on upstream switches, DSCs here can easily support fan-in that represents current signals from multiple upstream switches enter one downstream switch Fig.
This circuit also had the same function of logic gate circuit AND OR x,y ,z , whereas the computing speed was much faster than the reported two-layer logic gate circuits in solution 22 , With the abilities to perform basic functions including cascading, fan-in, and fan-out, theoretically the molecular switches can be used to build DSCs with arbitrary topologies. We next explored the circuit design strategy to perform arbitrary Boolean functions.
Inspired by the circuit proposed by Shannon 27 to solve symmetric functions, we developed a programmable switch canvas with complementary switch pairs Fig.
On the canvas, the connection between adjacent switches is configurable. A Boolean function is represented by a DSC by programmable routing on the switch canvas. Each line of the truth table is represented as a path on the switch canvas. As an example, we implemented a three-input voting logic by routing the switch canvas.
Thus, the layer number of the corresponding DSC was no more than the number of variables. We designed the sequence for each molecule according to requirements for cascade, fan-out, and fan-in as discussed above.
Using this strategy, the three-input voting function was demonstrated with a three-layer six-switch DSC Fig. We investigated the change of free energy during the reaction process for the DSC and logic gate circuit. We found that the magnitude of stepwise free-energy decrease is very close for all input combinations that lead to output in the DSC Fig.
In contrast, the logic gate circuit presented different trends of energy change for the four input combinations Fig. Previous study has shown that the reaction rate of SDR is positively correlated to energy change 30 , We hypothesize that the required time for current signal to arrive to reporter was less diverged using the DSC. As a result, the computing speed was improved. Numerical simulations Supplementary Fig. Experimental results Fig. These results suggested that even with the same molecular design, DSC showed higher computing speed and signal-to-noise ratio SNR than logic gates for some functions.
To exemplify arbitrary digital computing using DSCs, we further demonstrated a full-adder function. The required truth table of this function is shown in Fig. The direct mapping of the truth table on the programmable switch canvas generated a three-layer ten-switch DSC to implement the full-adder function Fig. The digital computing was performed with ten switch molecules and two reporter molecules to read out Carry and Sum output.
When it runs, there are up to 42 different DNA strands interacting in one test tube. Without the demand for dual-rail representation, the number of involved DNA molecules was decreased by nearly half than that of logic gate implementation Supplementary Fig. To further demonstrate the power of DSCs for performing complex digital tasks, we designed a DSC to compute the floor of the square root of a four-bit input Fig.
Compared with a dual-rail logic gate circuit to perform the same function Fig. We then compared our DSC with the previous ones using seesaw gates and single-stranded gates to solve four-bit square-rooting.
Prankster, inventor and juggler, the American mathematical engineer Claude Shannon had a hand in several innovations spanning across disciplines. Chief among them: a thesis that transformed modern computing. April 30, The juggling, suited man on the newest Google Doodle is American mathematician and engineer Claude Shannon. April 30, marks what would have been his th birthday. Working around the time of, and occasionally encountering, Einstein and Alan Turing, Dr.
Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. A symbolic analysis of relay and switching circuits Abstract: In the control and protective circuits of complex electrical systems it is frequently necessary to make intricate interconnections of relay contacts and switches. Examples of these circuits occur in automatic telephone exchanges, industrial motor-control equipment, and in almost any circuits designed to perform complex operations automatically. In this article a mathematical analysis of certain of the properties of such networks will be made.
In his thesis, Shannon, a dual degree graduate of the University of Michigan , proved that Boolean algebra  could be used to simplify the arrangement of the relays that were the building blocks of the electromechanical automatic telephone exchanges of the day. Shannon went on to prove that it should also be possible to use arrangements of relays to solve Boolean algebra problems. The utilization of the binary properties of electrical switches to perform logic functions is the basic concept that underlies all electronic digital computer designs. Shannon's thesis became the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II. At the time, the methods employed to design logic circuits were ad hoc in nature and lacked the theoretical discipline that Shannon's paper supplied to later projects. Psychologist Howard Gardner described Shannon's thesis as "possibly the most important, and also the most famous, master's thesis of the century".
Shannon while attending the Massachusetts Institute of Technology in In his thesis, Shannon, a dual degree graduate of the University of Michigan, proved that Boolean algebra could be used to simplify the arrangement of the relays that were the building blocks of the electromechanical automatic telephone exchanges of the day. Shannon went on to prove that it should also be possible to use arrangements of relays to solve Boolean algebra problems. The utilization of the binary properties of electrical switches to perform logic functions is the basic concept that underlies all electronic digital computer designs. Shannons thesis became the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II.
Коммандер. Нет. Сьюзан словно окаменела, ничего не понимая. Эхо выстрела слилось с царившим вокруг хаосом. Сознание гнало ее вперед, но ноги не слушались. Коммандер. Мгновение спустя она, спотыкаясь, карабкалась вверх по ступенькам, совершенно забыв о таящейся внизу опасности.
Через пять минут автобус, подпрыгивая, несся по темной сельской дороге. Беккер повернулся к панку. - Этот тарантас когда-нибудь остановится. - Еще пять миль. - Куда мы едем.
Танкадо использовал наживку для дурачков… и АНБ ее проглотило. Сверху раздался душераздирающий крик Стратмора. ГЛАВА 86 Когда Сьюзан, едва переводя дыхание, появилась в дверях кабинета коммандера, тот сидел за своим столом, сгорбившись и низко опустив голову, и в свете монитора она увидела капельки пота у него на лбу. Сирена выла не преставая.
У дверцы лифта есть код, - злорадно сказала Сьюзан. - Ну и проблема! - засмеялся Хейл. - Думаю, коммандер мне его откроет.
Беккер смотрел на него в полном недоумении. Человек сунул руку в карман и, вытащив пистолет, нацелил его Беккеру в голову. - El anillo. Внезапно Беккера охватило чувство, которого он никогда прежде не испытывал.
За едва заметным изгибом коридора Беккер услышал голоса. Он пошел на звук и уткнулся в стеклянную дверь, за которой, судя по доносящемуся оттуда шуму и гвалту, происходило нечто вроде драки. Преодолев отвращение, Беккер открыл дверь.
Иногда кому-то из стариков, которых посетил Святой Дух, становилось плохо. Только и делов - вывести человека на свежий воздух. Халохот отчаянно озирался, но Беккера нигде не было. Сотни людей стояли на коленях перед алтарем, принимая причастие. Может быть, Беккер был среди .
Халохот вырвался из вращающейся двери в тот момент, когда Беккер попытался завести мотоцикл. Убийца улыбнулся и начал поднимать пистолет. Заслонка. Беккер повернул рычажок под топливным баком и снова нажал на стартер.
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