# Logical Systems I

## Objectives

Describe digital systems through combinatorial Boolean algebraic expressions, truth tables, and schematics.

Apply methodology for synthesis of combinational circuits. Convert numbers between different base numbering, such as decimal, binary, hexadecimal and octal.

Analyze methods of modular decomposition of combinational circuits, including circuits for binary arithmetic. Apply techniques for expeditious design of counters.

Apply methodology for synthesis of synchronous state machines, starting from state diagrams. Implement digital systems with low/medium complexity using its decomposition.

## General characterization

10475

6.0

##### Responsible teacher

Pedro Alexandre da Costa Sousa, Ricardo Luís Rosa Jardim Gonçalves

Weekly - 4

Total - 63

Português

Not applicable

### Bibliography

1. Digital Logic Circuit Analysis & Design - Victor P. Nelson, H. Troy Nagle, J. David Irwin, Bill D. Carroll - Prentice Hall - ISBN 0-13-463894-8 2. Digital Design: Principles and Practice - John F. Wakerly - Prentice-Hall - ISBN 0-13-082599-9 3. Logic and Computer Design Fundamentals - M. Morris Mand, Charles Kime - Prentice-Hall - ISBN 0-13-182098-2 4. Circuitos Digitais e Microprocessadores - Herbert Taub - McGraw-Hill – ISBN 0-07-066595-8

### Teaching method

Lectures and practical classes

### Evaluation method

Theoretical evaluation:

2 tests each weighing 32.5% in the final grade. Minimum test average score is 9.5

Exam may be taken as an alternative to the tests, with a weight in the final grade of 65% minimum grade 9.5

Practical Evaluation:

Group work 35% in the final grade

In the case of passing tests, admission to the exam is an improvement and must be formally requested at the Faculty office.

## Subject matter

• Boolean algebra: Theorems; Truth tables. • Logical functions: Canonical representations; Function minimization; Karnaugh maps; • Numerical systems: conversions. • Binary arithmetic: Addition and Subtraction; Two''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''s-Complement; One''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''s-Complement; Multiplication and division. • Basic Combinatorial Circuits: Comparators; Encoders and decoders; Code Converters; Multiplexers and demultiplexers. • Memory elements: Concepts of latch and flip-flop; Flip-flop JK, D and T. • Sequential circuits: Synchronous and asynchronous circuits’ concepts; Registers. Counter design. • Synchronous state machines: State diagrams; Moore and Mealy circuits; Synthesis. • Specific devices: Memories. • Introduction to register transfer architectures: decomposition in control and data parts; introduction to microprocessors

## Programs

Programs where the course is taught: