Logics
Code  Completion  Credits  Range  Language 

17PBILOG  Z,ZK  4  2P+2L  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Biomedical Informatics
 Synopsis:

Logic system, logic circuit, logic function. Bool's algebra. Representation (models) of logic functions: expression/formula, table, cube, map, logical and functional schema, graph. Combinatorial and sequential logic nets. Huffman's schema. Minimization of expressions for combinatorial logical nets with one and more outputs. Normalized expressions, disjunctive and conjunctive forms. Minimization based on operations of Bool's algebra in expressions, in a unit cube, in a truth table (QuinMcCluskey's method), in a logic map  Karnaugh's maps.
Combinatorial logical terms, circuits and blocks. Synthesis of combinatorial logic circuits NOT, AND, OR, NAND, NOR. Synthesis of combinatorial logic circuits with limited number of inputs. Modeling of sequential behavior. Finite automata: Mealy and Moore automata. Memory circuits. Analysis and synthesis of synchronized sequential nets. Asynchronous sequential logic nets.
Predicate logic (PL): language, terms, formula, substitution and basic syntactic terms, semantics: structures for predicate logic, evaluation, evaluation of terms and formulas. Axiomatic system of PL: axioms, inference rules, concept of a proof, reasoning theorem.
 Requirements:

Basics of algebra
 Syllabus of lectures:

1.Logic system, logic circuit, logic function. Bool's algebra.
2.Representation (models) of logic functions: expression/formula, table, cube, map, logical and functional schema, graph.
3.Combinatorial and sequential logic nets. Huffman's schema.
4.Minimization of expressions for combinatorial logical nets with one and more outputs. Normalized expressions, disjunctive and conjunctive forms.
5.Minimization based on operations of Bool's algebra in expressions, in a unit cube.
6.Minimization based on operations of Bool's algebra in a truth table (QuinMcCluskey's method), in a logic map  Karnaugh's maps.
7.Combinatorial logical terms, circuits and blocks. Synthesis of combinatorial logic circuits NOT, AND, OR, NAND, NOR.
8.Synthesis of combinatorial logic circuits with limited number of inputs.
9.Modeling of sequential behavior. Finite automata: Mealy and Moore automata.
10.Memory circuits. Analysis and synthesis of synchronized sequential nets. Asynchronous sequential logic nets.
11.Predicate logic (PL): language, terms, formula, substitution and basic syntactic terms.
12.Semantics: structures for predicate logic, evaluation, evaluation of terms and formulas.
13.Axiomatic system of PL: axioms, inference rules, concept of a proof, reasoning theorem.
 Syllabus of tutorials:

1.Logic system, logic circuit, logic function. Bool's algebra.
2.Representation (models) of logic functions: expression/formula, table, cube, map, logical and functional schema, graph.
3.Combinatorial and sequential logic nets. Huffman's schema.
4.Minimization of expressions for combinatorial logical nets with one and more outputs. Normalized expressions, disjunctive and conjunctive forms.
5.Minimization based on operations of Bool's algebra in expressions, in a unit cube.
6.Minimization based on operations of Bool's algebra in a truth table (QuinMcCluskey's method), in a logic map  Karnaugh's maps.
7.Combinatorial logical terms, circuits and blocks. Synthesis of combinatorial logic circuits NOT, AND, OR, NAND, NOR.
8.Synthesis of combinatorial logic circuits with limited number of inputs.
9.Modeling of sequential behavior. Finite automata: Mealy and Moore automata.
10.Memory circuits. Analysis and synthesis of synchronized sequential nets. Asynchronous sequential logic nets.
11.Predicate logic (PL): language, terms, formula, substitution and basic syntactic terms.
12.Semantics: structures for predicate logic, evaluation, evaluation of terms and formulas.
13.Axiomatic system of PL: axioms, inference rules, concept of a proof, reasoning theorem.
 Study Objective:

The aim of the subject is to provide students with basics of logic, Bool's algebra, synthesis of logic circuits, finite automata and basics of predicate logics.
 Study materials:

[1] Gensler H.: Introduction to Logic, Routledge, ISBN13: 9780415226752, 2001.
[2] Gajski D. D.: Principles of Digital Design. PrenticeHall International, Inc. 1997.
[3] Wakerly, J. F.: Digital Design. Principles and Practices. Pearson Prentice Hall, New Jersey 2006.
[4] De Micheli G.: Synthesis and Optimization of Digital Circuits, McGrawHill Science, ISBN13: 9780070163331, 1994.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Biomedical Informatics  fulltime study (compulsory course)