Chapter 2
Cooperation Control Loops




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2.1
The Problem


2.2
The Concept
of the
Solution
2.3
Example:
Multiplication of
Binary Numbers


2.1 The Problem

After I had taught the subject of digital systems for many years at different universities, a departmental colleague once said to me, "I still do not understand why you are needed, since anyone can connect inputs of gates to outputs of gates, and anyone can write sequences of instructions." I told him: "Anyone can put bricks on top of each other. But not everyone can build a gothic cathedral using a million or more such bricks!"

What the program instructions are in the world of software, the gates are in the world of hardware. The cooperation of a few such elementary building blocks is easy to understand; but a system providing high level functions not only requires a few, but in simple cases thousands, and in most cases millions of such building blocks. Such systems cannot ever be designed from bottom up by starting with a few building blocks and combining them into manageable functional complexes in order to get building blocks for the next higher level, and so on. Instead, the design must be done from the top to the bottom, first considering the whole system as a black box and specifying its intended interaction with its environment. Subsequently, this initial black box must be decomposed into interacting subsystems on the next lower level. It is obvious that there can't be an algorithm for such a decomposition, but what I had been taught and learned in my studies about this problem lacked any methodology and seemed to me more like brilliant tinkering.

After my graduation in Electrical Engineering at the Technical University of Karlsruhe, I was given a research assistant position at the Institute of Information Processing. At that time , I assumed that among other things, I would learn how to design computer hardware and other digital control systems using a methodical process. I was convinced of the existence of rules which can guide designers in their search for suitable decompositions of specified black boxes. Therefore, at the very beginning of my time as an assistant, I began to look for such rules. But I found nothing useful neither in our institute nor in the technical literature.

However, I never would have thought that even today, about fifty years later, I would still not find any references to such rules in the professional literature. For this means that no one except me sees a need for such rules. Perhaps I have to accept the fact that the availability of powerful software tools for the simulation of digital electronic systems represents such a far-reaching support of the “brilliant tinkering” that the demand I see cannot be seen by anyone else.

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