Analog and Digital Computation:
It is difficult to know whether the modern digital computer, and its Von Neumann architecture, were ever intended to interface to the real world. A computer is, by definition, a "reckoning machine" and certainly its original designers went to great lengths to make it into a device that could carry out repetitive computations and provide a limited amount of human reasoning. The analog computer, on the other hand, has always been closely associated with the control of physical systems, but has never been able to provide the reckoning ability that we associate with the digital computer. Analog computers no longer play any significant role in modern engineering, and so, this book is predominantly about digital computers and the problems that we face in connecting them to engineering systems.
It is interesting to note that when we use digital computers as islands of intelligence (that is, on their own), we find that their capabilities are only restricted by our own reasoning ability (that is, our ability to generate software) and by the speed at which computers can carry out the reasoning that we have instilled via our software. However, when we wish to interface computers to the real world (so that they can use their programmed reasoning to control a physical system) we find that our reasoning needs to be supplemented with an understanding of electronics, physics and engineering design principles before we can generate sensible solutions.
It is altogether likely that any computer programmer, with no knowledge of computer architecture or electronics, could create a working computer control system. Certainly, there are a sufficient number of commercially available, "black-box" solutions to assist in interfacing computers to external systems. The problem with using such solutions, without a proper understanding of the design principles behind them, is that sooner or later the seemingly minor problems that arise (system instability, unwanted spurious signals, irregular behaviour, etc.) become insoluble.
The first issue that really needs to be addressed is that of the digital and analog computing domains. In all our "Newtonian" time-frames, the world is essentially analog in nature. Physical quantities do not change from one energy level to another in zero time - there is normally a continuous transition from one state to another, rather than a quantum variation. One may well ask why, if the world is essentially analog, have we chosen to discard the concept of analog computing and replace it with digital (quantum) computing. There are many reasons why analog computers were discontinued in the 1970s. These include:
• Accuracy
• Size
• Power consumption
• Cost.
Underlying all the problems in analog computing is the issue of representing quantities accurately. Consider an analog computer that is required to take in two numbers (between zero and ten) and add them together to achieve a given result. How is this achieved? We could represent each of the inputs and outputs with a voltage and use a circuit to electrically add the inputs to provide the required output. This is shown in Figure:
we would assume that if Input A is equal to 5 volts and Input B is equal to 2 volts, then the output would be equal to 7 volts. What happens however, if:
• Input A = 5.001322447 volts
• Input B = 1.999933821 volts ?
The answer to this question really depends upon how accurately we can design and fabricate our analog addition circuit. In engineering, we know that accuracy in setting or measuring energy levels normally equates to higher complexity and higher cost. This is certainly true in electronic circuits.
It is difficult to know whether the modern digital computer, and its Von Neumann architecture, were ever intended to interface to the real world. A computer is, by definition, a "reckoning machine" and certainly its original designers went to great lengths to make it into a device that could carry out repetitive computations and provide a limited amount of human reasoning. The analog computer, on the other hand, has always been closely associated with the control of physical systems, but has never been able to provide the reckoning ability that we associate with the digital computer. Analog computers no longer play any significant role in modern engineering, and so, this book is predominantly about digital computers and the problems that we face in connecting them to engineering systems.
It is interesting to note that when we use digital computers as islands of intelligence (that is, on their own), we find that their capabilities are only restricted by our own reasoning ability (that is, our ability to generate software) and by the speed at which computers can carry out the reasoning that we have instilled via our software. However, when we wish to interface computers to the real world (so that they can use their programmed reasoning to control a physical system) we find that our reasoning needs to be supplemented with an understanding of electronics, physics and engineering design principles before we can generate sensible solutions.
It is altogether likely that any computer programmer, with no knowledge of computer architecture or electronics, could create a working computer control system. Certainly, there are a sufficient number of commercially available, "black-box" solutions to assist in interfacing computers to external systems. The problem with using such solutions, without a proper understanding of the design principles behind them, is that sooner or later the seemingly minor problems that arise (system instability, unwanted spurious signals, irregular behaviour, etc.) become insoluble.
The first issue that really needs to be addressed is that of the digital and analog computing domains. In all our "Newtonian" time-frames, the world is essentially analog in nature. Physical quantities do not change from one energy level to another in zero time - there is normally a continuous transition from one state to another, rather than a quantum variation. One may well ask why, if the world is essentially analog, have we chosen to discard the concept of analog computing and replace it with digital (quantum) computing. There are many reasons why analog computers were discontinued in the 1970s. These include:
• Accuracy
• Size
• Power consumption
• Cost.
Underlying all the problems in analog computing is the issue of representing quantities accurately. Consider an analog computer that is required to take in two numbers (between zero and ten) and add them together to achieve a given result. How is this achieved? We could represent each of the inputs and outputs with a voltage and use a circuit to electrically add the inputs to provide the required output. This is shown in Figure:
we would assume that if Input A is equal to 5 volts and Input B is equal to 2 volts, then the output would be equal to 7 volts. What happens however, if:• Input A = 5.001322447 volts
• Input B = 1.999933821 volts ?
The answer to this question really depends upon how accurately we can design and fabricate our analog addition circuit. In engineering, we know that accuracy in setting or measuring energy levels normally equates to higher complexity and higher cost. This is certainly true in electronic circuits.
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