In fact, calculation underlies many activities that are not normally thought of as mathematical. Walking across a room, for instance, requires many complex, albeit subconscious, calculations. Computers, too, have proved capable of solving a vast array of problems, from balancing a checkbook to even—in the form of guidance systems for robots—walking across a room. Before the true power of computing could be realized, therefore, the naive view of calculation had to be overcome. The inventors who laboured to bring the computer into the world had to learn that the thing they were inventing was not just a number cruncher, not merely a calculator. For example, they had to learn that it was not necessary to invent a new computer for every new calculation and that a computer could be designed to solve numerous problems, even problems not yet imagined when the computer was built.

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## History of computing

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We analyse the pros and cons of analog versus digital computation in living cells. Our analysis is based on fundamental laws of noise in gene and protein expression, which set limits on the energy, time, space, molecular count and part-count resources needed to compute at a given level of precision.

We conclude that analog computation is significantly more efficient in its use of resources than deterministic digital computation even at relatively high levels of precision in the cell. Based on this analysis, we conclude that synthetic biology must use analog, collective analog, probabilistic and hybrid analog—digital computational approaches; otherwise, even relatively simple synthetic computations in cells such as addition will exceed energy and molecular-count budgets.

We present schematics for efficiently representing analog DNA—protein computation in cells. Analog electronic flow in subthreshold transistors and analog molecular flux in chemical reactions obey Boltzmann exponential laws of thermodynamics and are described by astoundingly similar logarithmic electrochemical potentials.

Therefore, cytomorphic circuits can help to map circuit designs between electronic and biochemical domains. We review recent work that uses positive-feedback linearization circuits to architect wide-dynamic-range logarithmic analog computation in Escherichia coli using three transcription factors, nearly two orders of magnitude more efficient in parts than prior digital implementations. Based on a single amino acid among thousands of proteins, immune cells must collectively decide whether a given molecule or molecular fragment is from a friend or foe, and if they err in their decision by even a tiny amount, autoimmune disease, infectious disease, or cancer could originate with high probability every day [ 2 ].

The field of synthetic biology attempts to transfer engineering design principles and experimental techniques into rational biological design [ 4 — 8 ]. It represents the ultimate limit of Moore's law: computation with the molecules themselves at the nanoscale through the use of controlled biochemistry and biophysics.

The self-organizing amorphous soup in a cell processes information while it destroys, repairs and rebuilds the structures needed to do so.

It is remarkable that it does so through a self-aligned nanotechnology with no explicit wiring. These reactions cause transformations of state, which are necessary for computation to occur.

While significant progress has been made w. One important reason for this failure has been its overemphasis on digital paradigms of thought: because digital design is relatively straightforward and scalable, and because molecules and atoms are discrete, it is logical to assume that engineering biology as we engineer switches and logic gates today will bear fruit.

The sheer force and powerful success of digital computation over the past few decades has been impressive. Nature is not purely digital. While molecules are discrete and digital, all molecular interactions that lead to computation, e. Depending on one's point of view, computation in a cell is owing to lots of probabilistic digital events or owing to continuous analog computation with noise.

Both views are equivalent. Indeed, the noise in analog systems is related to the Poisson rate of the underlying probabilistic digital events; the shot noise of thermally generated diffusion currents caused by these Poisson processes generates noise in all analog systems [ 1 , 11 ].

Synthetic biology has now recognized that the signals in cells are stochastic noisy and analog graded in their nature [ 12 ]. While logic basis functions and positive-feedback loops are certainly used by cells to make irreversible decisions, to organize sequential computation and to perform signal restoration, analog computation is extremely important for the cell's incredible efficiency w.

The efficiency arises because analog computation can use powerful input—output basis functions in the technology for addition, multiplication, exponentials, logarithms, power laws and spatio-temporal filtering, which are already naturally present in the differential equations of physics and chemistry. Therefore, it does not need to re-invent these input—output basis functions from scratch with logic.

For example, the production fluxes of two genes that encode the synthesis of a common output protein automatically perform addition via a molecular version of Kirchoff's current law without the need for tedious logic; the binding of two molecules provides a basis function for multiplication; the binding of identical molecules in a dimer provides basis functions for computing squares or square roots; molecular degradation naturally provides basis functions for temporal filtering; diffusion naturally provides a basis function for spatial filtering.

The pioneers of digital computation, John von Neumann and Alan Turing, appreciated the great power of analog computation and were investigating it intensely to cope with the limitations of using only logic to compute. Near the end of their lives, they were working on understanding analog computation in brains [ 15 ] and in cells [ 16 ], respectively. Analog computation has long been appreciated to be important in the brain [ 17 ], but its importance in cells has been greatly underappreciated.

In this article, we begin by describing analog circuit schematics for a single gene, which provide a foundation for the rest of the article and a quick introduction to the computational basics of cell biology. Then, we review the pros and cons of analog versus digital computation with a focus on computation in living cells.

This simple example will help us to analyse general trade-offs w. The analysis will show that, below a certain crossover computational precision, it is highly advantageous to compute in an analog fashion to reduce the energy, part count or number of molecules and thus volume or space needed for the computation.

It is therefore not surprising that cells exploit analog computation to perform their moderate-precision computations. Other work has also shown that collective analog computation can use several moderate-precision interacting analog units to architect computations of arbitrary precision, e.

Collective analog systems can also architect arbitrary complex computations through interactions of moderate-precision analog computational units in the brain and in the cell. In analog computation, every signal and every device are not reliable, but important final or decisive outputs are. To attenuate noise, analog computation invariably relies on feedback loops, the wise use of energy, time or space resources to improve precision via averaging at critical state variables and reference inputs, learning and adaptation, nonlinearities, such as thresholding or digitization, or invariants and attractors in the analog dynamical system that cause it to equilibrate to restorative discrete outputs.

Though noise limits information capacity, it can sometimes be beneficial for searching intractable combinatorial spaces and for improving the detection of signals by phenomena such as stochastic resonance. How do we transfer analog circuits in electronics to analog circuits in cells? Fortunately, there is a deep connection between electronics and chemistry, which greatly aids the design of analog circuit motifs and analog computation in synthetic biology.

By contrast, a prior in vitro 2-bit-precise digital square-root computation required DNA-based parts [ 23 ]. Another circuit described in [ 22 ] was able to accurately compute the logarithmic ratio of two molecular concentrations over four orders of magnitude. The latter circuit used novel positive-feedback linearization circuits, similar to those used in my laboratory in log-domain subthreshold electronic amplifiers in the past [ 24 ].

The genetic circuits described in [ 22 ] may have wide applications for wide-dynamic-range molecular sensing, complex computation with few parts in biotechnology and medicine, and for the fine control of gene expression.

The cytomorphic mapping. The analog circuits approach described in this article may enable large-scale design and analysis in synthetic and systems biology, which is faithful to how messy analog biology works, quite different from clean, well-defined digital design. It may enable several applications in synthetic biology, wherein, just as in electronics today, all applications benefit from low-part-count, low energy usage and clever analog feedback loops to improve performance.

Analog synthetic biology can serve to make synthetic computation practical because it does not impose man-made views of what computation should be in the cell, but computes in a fashion that is similar to the way the cell itself computes. The success of analog circuit design arises in large part from having efficient pictorial representations that are more intuitive to humans than reams of differential equations. Intuition aids design. The analog circuit schematics nevertheless preserve most of the needed mathematical information in the equation as labelled parameters, such that analysis can aid design.

Similarly, the transcription factor, V rep , which normally binds DNA and represses transcription is de-repressed by V rep ind , such that the net effect of V rep ind is to also stimulate gene expression in this example. Repression is always indicated by the T-shaped symbols and activation is always indicated by arrow inputs at the border of the multiplier or at the border of the dependent current generator.

Inducer inputs are typically small-molecule external inputs to the cell that diffuse into it and bind internal transcription factors within the cell. In bacteria and yeast, it is not common to have more than two controlling inputs at a DNA promoter, but mammalian cells can have several controlling inputs.

The dependent generator will have as many inputs as the DNA promoter. Analog schematic for genetic circuits. The resistor R prot degrades the protein such that the synthesis translation current balances the protein degradation current and V prot reaches a steady-state value. They also match experimental input—output data gathered from non-pathogenic E. As R prot is typically much greater than R mRNA , it is common to assume that the mRNA dynamics are relatively instantaneous compared with protein dynamics [ 31 ].

It allows one to focus on a protein-input—protein-output point of view. Robustness—efficiency trade-offs are ubiquitous in all engineering systems [ 33 ] and are at the heart of all good engineering design.

Therefore, we shall begin by deriving some important results regarding molecular noise in cells. There are a lot of experimental measurements and numbers available for S.

Hence, we shall use it as our representative cell. The total noise of the protein signal is owing to the net mRNA noise content as well as that owing to the intrinsic shot noise of the Poisson protein molecular flux. That is,. The output signal-to-noise ratio S N is then given by. The equivalent informational bit precision [ 39 ] is given by. Protein and mRNA molecules have to be constantly synthesized to counter their degradation, and this synthesis consumes power.

The synthesis power is provided by the hydrolysis of several molecules of adenosine triphosphate ATP , the universal energy-providing molecular currency of cells. ATP hydrolysis enables various processes in transcription and translation to move forward in a nearly irreversible fashion [ 2 ]. Hence, the power consumption needed to charge or maintain a protein signal level of N prot is given by. Such resource—precision relationships are universal and can be found in neurobiological, electrical, mechanical and all systems [ 1 ].

Intuitively, to be fast and precise, a scenario that maximizes information, a system consumes power. For example, slow-and-parallel systems with moderate local precision lead to very power efficient systems, both in the brain and in electronics [ 1 ].

Equation 3. Simple differentiation reveals that this optimum occurs when. To implement a molecular adder via analog computation is simple: we have the two inputs to be added; each regulates the expression of a common output protein from independent genetic promoters. During synthesis, the two molecular fluxes will automatically add to create the common output protein, which is the answer.

To enable linear analog operation and avoid saturated digital operation, the input proteins must operate at a concentration that is well below K d , the binding constant of the DNA promoter.

As the input and output concentrations increase, the input and output noise reduce, the precision of the computation improves, but at the price of higher molecular count and higher power consumption.

The computation only requires two genetic parts, independent of precision or molecular count, which makes it practical to implement. To estimate the costs of this computation, we shall assume, for simplicity, that the input and output molecular counts are equal promoters with a net gain of 1 , which enable both the precision of the input and output to concomitantly scale with the overall needs of the computational precision.

A proportionate gain scaling between the input and output is also possible but adds complexity while obscuring the key insights that we want to emphasize. Analogous to how mRNA noise flux propagates to protein outputs and increases noise, the input noise flux propagates to the adder output. Thus, the adder will have twice the squared noise as would be expected from its output molecular count alone. Therefore, to preserve the S N all molecular counts must be increased by a factor of 2 at the input and output, leading to a four times larger total molecular count for the same S N.

To minimize the power consumption, digital logic gates must have as small a protein copy number for high values as possible. The parameter K d is an equilibrium chemical binding constant that effectively behaves as a threshold voltage in the digital operation.

Note that K d variations among gates can be static or dynamic owing to loading and crosstalk. The exact value of N digLO does not matter too much as long as it is sufficiently low. Thus, we shall, for simplicity, ignore dimerization and polymerization effects that are, to first order, neutral w.

For simplicity, we shall also assume that any logic gate operates at saturated values that are the same as that of its inputs such that logic gates can be easily composed and cascaded similar to that in today's electronic systems.

Otherwise, digital implementations will require molecular gain and attenuation between logic stages. So, our assumption is generous to digital implementations. If the probabilities of low and high values in the adder are p low and p high , respectively, with corresponding values of N digHI and N digLO for the protein state variables, then the resource—precision equations for the molecular count, N D , and the power consumption, P D , of the digital adder can be computed to be.

Analog Devices Waveform. Digital output devices control the state of the digital signals and can transition from one digital pulse to another. Abstract: Techniques for duplex communication and power transfer across an isolator are provided. Drawing electrical diagram in order to illustrate.

## Introduction to Computer Information Systems/Print version

This website uses cookies to ensure you get the best experience on our website. To establish the connection to the application environment, customer-specific serial interfaces are also possible. Analog motion controllers, as still used for piezo-based positioning systems, are equipped with an analog proportional, integral, and differential PID controller and linearization processes through which the input voltage corresponds as close as possible to the target position. The resolution and process time thus depend directly on the components used and allow subnanometer motion and real-time command. In addition, PI offers an analog interface for many controls as connection to external operating elements such as joysticks. Real-time Fieldbus interfaces are often used on automated production lines. Real time means that not only the transmission itself is secured but also the chronological sequence.

## EE Courses

A computer is a machine for manipulating data according to a list of instructions. Computers take numerous physical forms. Early electronic computers were the size of a large room, consuming as much power as several hundred modern personal computers. Today, computers can be made small enough to fit into a wrist watch and be powered from a watch battery. Society has come to recognize personal computers and their portable equivalent, the laptop computer, as icons of the information age; they are what most people think of as "a computer. Embedded computers are small, simple devices that are often used to control other devices—for example, they may be found in machines ranging from fighter aircraft to industrial robots, digital cameras, and even children's toys. The ability to store and execute programs makes computers extremely versatile and distinguishes them from calculators.

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That same year in Germany, engineer Konrad Zuse built his Z2 computer, also using telephone company relays. Their first product, the HP A Audio Oscillator, rapidly became a popular piece of test equipment for engineers. In , Bell Telephone Laboratories completes this calculator, designed by scientist George Stibitz. Stibitz stunned the group by performing calculations remotely on the CNC located in New York City using a Teletype terminal connected via to New York over special telephone lines. This is likely the first example of remote access computing. The Z3, an early computer built by German engineer Konrad Zuse working in complete isolation from developments elsewhere, uses 2, relays, performs floating point binary arithmetic, and has a bit word length. The Z3 was used for aerodynamic calculations but was destroyed in a bombing raid on Berlin in late Zuse later supervised a reconstruction of the Z3 in the s, which is currently on display at the Deutsches Museum in Munich. Hundreds of allied bombes were built in order to determine the daily rotor start positions of Enigma cipher machines, which in turn allowed the Allies to decrypt German messages.

## Digital and Analog Interfaces

The history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers. Before the 20th century, most calculations were done by humans. Early mechanical tools to help humans with digital calculations, like the abacus , were called "calculating machines", called by proprietary names, or referred to as calculators. The machine operator was called the computer.

Change direction of binary code through. Welcome to our site, dear reader! All content included on our site, such as text, images, digital downloads and other, is the property of it's content suppliers and protected by US and international copyright laws. This place becomes a part of a latent image. Section of the Act specifies the basic terms under which digital television will move forward. Paul Horowitz has a nice desc. Consequently digital logic circuits are ideal for the internal electronics. To recover mtfrom st, we require the use of coherent detection. Linear computer elements perform the operations of summation, integration, changes of sign, multiplication by a constant, and others. In electronic circuits, there are many electronic symbols that are used to represent or identify a basic electronic or electrical device. Recent evidence shows it could date back to BC or beyond.

## Analog Devices Waveform

Account Options Sign in. Federal Highway Administration. Selected pages Page Page How a dualdrum paver operates. Fuel and time consumption rales for trucks in freigbt service. Errata see vol 30 No 11 pp The economic cost of traffic accidents in relation to highway.

## Being Analog

Computers Computer is a machine for performing calculations automatically. An expert at calculation or at operating calculating machines. A machine that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Memory and Processing. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures or algorithms that underlie the acquisition, representation , processing , storage , communication of, and access to information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale.

## History of Computers

Today's world runs on computers. Nearly every aspect of modern life involves computers in some form or fashion. As technology is advancing, the scale of computer use is increasing. Computer users include both corporate companies and individuals.

## Glossary Of Technical Terms

An analog computer or analogue computer is a type of computer that uses the continuously changeable aspects of physical phenomena such as electrical , mechanical , or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude. Analog computers can have a very wide range of complexity. Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the s and s, although remained in use in some specific applications, such as aircraft flight simulators , the flight computer in aircraft , and for teaching control systems in universities.

## History of computing hardware

We analyse the pros and cons of analog versus digital computation in living cells. Our analysis is based on fundamental laws of noise in gene and protein expression, which set limits on the energy, time, space, molecular count and part-count resources needed to compute at a given level of precision.

## Analog computer

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