### Digitaltechnik

 Vortragssprache Deutsch

# Digital Technology

### Goals

The goal is to relay the theoretical fundamentals.

### Contents

#### Lecture

This lecture presents an introduction to the important theoretical fundamentals of digital system design, which is scheduled for the students in the first semester of Electrical Engineering.  Since the students are not able to design based upon knowledge of circuit technology, the lecture concentrates on abstract models for behaviours and structures.  In addition the lecture will also relay the fundamentals, which are needed in other lectures.

At first the lecture delves into important conceptual information and shows, that digital system design is a special technical solution for the treatment of information.  After this the concept of a system will be introduced and clarified, in that complex systems constantly require a hierarchical partitioning in order to be able to understand and design them.  Based on this it can be concluded then that designing can be constantly understood as a repeated transformation from descriptions of behaviour to descriptions of structure.

The terms message and signal are subject matter of a further chapter.  Starting from time and amplitude continuous signals, simple time and value discrete binary signal representations will be introduced, and out of this, more complex signal forms as well.

The representation of information by signals presupposes or implies an "agreement of allocation" between distinguishable elements of information representation and signal representation, the so-called codes.  Therefore the lecture delivers the fundamental concepts of codes & coding and describes a few important classes & types of codes, which serve some of the following uses: analog/digital conversion for interfaces, error detection & error correction for numerical purposes, and optimal representation of information and/or signals. Code conversion and related topics finalize the consideration of this topic.

Formal and mathematical fundamentals will be treated in an extensive chapter. To begin the subject matter of the lecture is comprised of sets and quantities, the operations on these quantities, and the relations between set elements. Afterwards follows several fundamentals of graph theory and finally it will be shown that logic algebra can serve as a basis for special Boolean algebra. Building upon the associated rules the concept of switching functions, their graphical representation and classification up to the standard theories, and important basis systems for the representation of Boolean expressions will be derived and considered.  Expansion theory, the computation with allocation blocks & terms, as well as measurements for minimization are further topics of this chapter.

Having the formal basics available, applicable technical components and structures will be developed on the basis of binary switches, which allow for an direct conversion of formal relationships into solutions. Gates, circuit networks, and synchronized sequential circuits, as well as specially derived functional units such as counters, registers, and digital memories then lead to complex structures, whereupon the "All-purpose Computer" from J. von Neumann will be particularly dealt with.

#### Exercises

To accompany the lecture material, assignments and the corresponding solutions will be given out and discussed during lecture hall exercises. In the last third of the semester, however, replacing these will be small group exercises done on computer, through which digital circuits and their pattern of behaviour will be modelled and simulated with the help of the program LogicWorks.

### Allgemeine Informationen

Das Material zur Vorlesung Digitaltechnik befindet sich auf ILIAS, das Sie unter https://ilias.studium.kit.edu erreichen können. Dort finden Sie im Kursbereich die Vorlesung "Digitaltechnik".

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