Lecture

Optimizing Logic Functions

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In course

EE-110: Logic systems (for MT)

Ce cours couvre les fondements des systèmes numériques. Sur la base d'algèbre Booléenne et de circuitscombinatoires et séquentiels incluant les machines d'états finis, les methodes d'analyse et de synthèse de systèmelogiques sont étudiées et appliquée ...

Description

This lecture covers the optimization of logic functions using Karnaugh diagrams with examples of 3 and 4 variables. It explains how to identify valid groups, the importance of minimizing equations, and dealing with incomplete defined functions.

Instructor

Alexandre Schmid

Alexandre Schmid received the M.Sc. degree in microengineering and the Ph.D. degree in electrical engineering from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1994 and 2000, respectively. Since 1994, he has been with the EPFL, working with the Integrated Systems Laboratory as a Research and Teaching Assistant, and with the Electronics Laboratories as a Postdoctoral Fellow. In 2002, he was a Senior Research Associate with the Microelectronic Systems Laboratory, where he has been conducting research in the fields of bioelectronic interfaces and implantable biomedical electronics, nonconventional signal processing and neuromorphic hardware, and reliability of nanoelectronic devices, and also teaches with the Microengineering and Electrical Engineering Departments of EPFL. Since 2011, he is a Maître d'Enseignement et de Recherche (MER) Faculty Member with EPFL. He is a coauthor of two books, Reliability of Nanoscale Circuits and Systems, Methodologies and Circuit Architectures, Springer, 2011, and Wireless Cortical Implantable Systems, Springer, 2013, and a coeditor of one book, as well as over 100 articles published in journals and conferences. Dr. Schmid has served as the General Chair of the Fourth International Conference on Nano-Networks in 2009 and has been serving as an Associate Editor of the Institute of Electrical, Information, and Communication Engineers Electronics Express since 2009.

Official source

Ontological neighbourhood

Logic

Classical logic: First-order logic

Related concepts (32)

Truth function

In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly one truth value; and inputting the same truth value(s) will always output the same truth value.

Karnaugh map

The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 logical diagram aka Marquand diagram but with a focus now set on its utility for switching circuits. Veitch charts are also known as Marquand–Veitch diagrams or, rarely, as Svoboda charts, and Karnaugh maps as Karnaugh–Veitch maps (KV maps).

Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Iranian Azerbaijani mathematician Lotfi Zadeh.

Mathematical logic

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.

Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.

Related lectures (64)

Boolean Algebra: Properties and Optimization

Covers Boolean algebra properties, optimization techniques, and the importance of valid groups in Karnaugh maps.

Logic Synthesis: Designing Efficient Digital Circuits

Discusses logic synthesis techniques for designing efficient digital circuits from functional descriptions and truth tables.

Boolean Algebra: Properties and Optimization

Explores Boolean algebra properties and optimization techniques using Karnaugh diagrams and De Morgan's theorems.

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Boolean Algebra: Properties and Theorems