Switching Theory and Logical Design

Aim

The purpose of the course is to provide a theoretical and practical basis for the construction and troubleshooting of digital systems. After completing the course, the student should be able to,

• translate a problem statement into a theoretical model for digital circuits
• apply structured methods for the analysis and synthesis of digital circuits
• translate a design into functioning hardware
• verify the hardware against the original problem description.

Assessment Criteria

The learning outcomes are specified according to the following assessment criteria. The student should be able to:

• Translate a problem statement into a theoretical model for digital circuits.Construct a truth table for a combinational circuit based on a given problem statement.Create a state graph for a synchronous sequential circuit based on a problem description, considering a timing diagram.Determine whether a sequential circuit should be realized according to the Mealy or Moore model.Model small digital circuits using a hardware description language.
• Apply structured methods for the analysis and synthesis of digital circuits.Design combinational circuits using minimal combinatorial expressions tailored to available gates and programmable memories.Design synchronous sequential circuits according to Mealy and Moore models.Design synchronous digital circuits using common digital building blocks.Synthesize a circuit given a model in a hardware description language.Calculate the truth table for a combinational circuit.Calculate the state diagram for a sequential circuit and, given an input sequence, determine the output sequence for the system.
• Translate a design into functional hardware.Implement combinational circuits and synchronous sequential circuits in hardware.
• Verify the hardware against the original problem description.Verify solutions against formal descriptions such as truth tables, state diagrams, and timing diagrams.Debug digital circuits.

Content

Lectures, lessons, and laboratory work cover:

• Number representations, conversions, and codes.
• Algebra: Boolean algebra and XOR.
• Digital building blocks: gates, inverters, adders, comparators, decoders, demultiplexers, multiplexers, memories, programmable logic, D-flip-flops, counters, registers, and shift registers.
• Tri-state.
• Synthesis of combinational circuits: minimization, Karnaugh maps, incompletely specified circuits, circuits with multiple outputs.
• Sequential circuits: synchronicity-asynchronicity, states, state-space models Mealy and Moore, and state diagrams.
• Synthesis of synchronous sequential circuits, handling of asynchronous inputs to synchronous systems, and state initialization.
• Synthesis with counters, registers, and shift registers.
• Modeling in hardware description languages and synthesis in programmable logic.