Combinatorial and sequential logic

This module covers the analysis and synthesis of combinational and sequential logic circuits. These circuits are the fundamental elements of all current digital systems (CPUs, GPUs, microcontrollers, etc.). This module serves as a prerequisite for all the digital electronics and microcomputing modules in the course.  

Module organization :

General organization

6 lectures (6 x 1h20 = 6h40)
4 practical sessions (4 x 1h20 = 5h20)
4 practical sessions (4 x 4h00 = 16h00)2 practical work (2 x 4h = 8h)

Lectures

The aim of the lectures is to provide the theoretical underpinnings and a few keys to the practical aspects, so that you can tackle the tutorials and practical exercises with confidence.

Part 1: Information representation + binary arithmetic
Part 2: Boolean algebra
Part 3: Combinatorial circuits
Part 4: Sequential circuits

TD applications of the course

The course application tutorials use exercises and examples to explore the concepts covered in the course in greater depth.

TD on machine

The aim of the TD and TDM sessions is to provide an introduction to digital circuit design in VHDL. The 4 sessions are guided by the teacher and cover the fundamental principles of synchronous digital circuit design using the VHDL language.

NB: TDM begins with an introduction to the use of Synopsys Design Compiler for logic circuit synthesis and Modelsim for logic simulation.

Practical work (TP)

Practical work is carried out in the same way as CT, with a slightly greater degree of autonomy.

List of skills to be acquired during this module : 

Number representation

• Convert any natural integer from one base to another.
• Represent a relative integer in base 2 using 2's complement.
• Add, subtract and multiply two numbers in base 2

Boolean algebra

• Represent a logic function in its three possible forms:

1. logical equation, algebraic equations (canonical and simplified forms)
2. tables of values (truth tables and Karnaugh tables)
3. logic circuits

• Switch from one representation of a logic function to another using Boolean algebra

• Use algebraic and graphical tools (Karnaugh chart) to simplify a logical equation.

Combinatorial logic

• Logic operation of elementary combinatorial circuits (elementary logic gates, multiplexers, adders, subtracters, comparators, decoders, etc.)

• Combine combinatorial circuits to design more complex combinatorial systems from specifications.

• Analyze the logic behavior of a combinational circuit made up of elementary circuits.

Sequential logic

• Design the circuit for a buffer or shift register based on D Flip-Flops.

• Design a binary counter circuit from a specification.
• Design a state machine circuit from a specification.
• Use multiplexers to modify the behavior of a sequential circuit (activation, initialization, loading, etc.).
• Draw a chronogram of the logic signals of a digital circuit containing sequential and combinatorial logic.

VHDL

• Know the general structure of a VHDL file (entity, architecture, declaration zone, etc.).
• Use combinatorial or sequential processes wisely.
• Describe the behavior of basic digital circuits from a circuit diagram or specifications.
• Use the numeric_std library to describe an arithmetic operator.
• Instantiate an existing entity in another.
• Describe a testbench for a given VHDL entity.

Simulation and synthesis

• Use a logic simulation and logic synthesis tool for a given VHDL description.
• Analyze error messages provided by the tool to correct an erroneous VHDL description.
• Create a project and run the logic simulation of a VHDL description using a testbench
• Keep your work directory tree organized and tidy.
• Check the consistency between a logic circuit generated by a logic synthesis tool and its VHDL description.

None

Digital electronics.

TD and TP handouts.

Moodle platform.