Digital Circuits

The general idea that is the motif for this lecture is to show what are the major components and how to design computer subsystems. The lecture starts with mathematical foundations, traverses automatons without and with memory, and ends with the design of digital systems. Moreover, the circuits integrated to a higher extent or more complex systems are designed using already introduced components. For instance, a D flip-flop is designed using gates, then in turn functional blocks, such as counters or registers, are designed using flip-flops, and finally functional blocks are used to construct digital systems. In this way no phase of integration is left out. The students should be able to design circuits and systems using elements of any scale of integration according to the needs of a project. Moreover, different approaches to designing the same circuits or systems are explained. All the concepts are explained explicitly showing the design process by simple yet real engineering examples. The lecture is supplemented by hands-on laboratory training sessions.


Lecture contents

1. Algebraic notation and Boolean algebra, simple problem solved intuitively showing the necessity of minimization


2. Combinational circuits , Natural Binary Code (NBC), Grey`s code, adjacency, partial adjacency, Karnaugh maps, implicants and implicents, minimization using Karnaugh maps, sum of products (SOP) form, product of sums (POS) form; AND, OR, NOT, NAND and NOR gates; Functionally complete systems; prohibition, factorization


3. Minimization using Quine`s and McCluskey`s algorithms; Iterative circuits; Hazard


4. Design of combinational circuits using: multiplexers,demultiplexers, encoders, decoders, programable logic arrays (PAL, GAL, PLA), read only memories (ROM),


5. Sequential circuits; Concept of internal state in an automaton with memory; Moore and Mealy automatons; natural language description, timing plots, graphs


6. Synchronous automatons; equivalence of automatons; minimisation of the number of internal states; Graph of a synchronous automaton


7. Complete and incomplete synchronous automatons; transfer and output tables; minimisation for complete and incomplete automatons; coding of internal states; realisation using D flip-flops and JK flip-flops
8. Asynchronous automatons; transfer and output tables; timing plot of an asynchronous automaton; stable states and transition states; minimization of a primary automaton graph of an asynchronous automaton; coding of states (hypercubes); races


9. Realisation using gates and R-S flip-flops;


10. Functional blocks; Design of a selected functional block using flip-flops and gates; Types of inputs to functional blocks (static, dynamic, enabling); types of functional blocks; registers; counters; MUX, DEMUX, 3-state gates; comparators; adders; ALU


11. Representation of numbers. Codes: positional number systems, signed-magnitude, complement number systems, radix-complement representation, two`s complement, diminished radix complement, ones` complement


12. Digital systems. Decomposition of a digital system into operational and control subsystems; design of the operational subsystem using functional blocks;


13. Control subsystem; flow chart of the control subsystem; conversion of a flow chart into a Moore/Mealy automaton graph; minimal synchronous automaton realisation; sequencer realisation


14. Conversion into a microprogrammed controller; timing problems (clocks); power up initialisation of the system; Interfacing to external systems (e.g. handshaking)


15. Concurrent digital circuits; Petri nets (places, transitions, marking, firing sequences); Transition from a Petri net to a control circuit

1. Introduction


2. Combinational circuits


3. Synchronous machines


4. Asynchronous machines


5. MSI circuits


6. Microprogramming

1. Wakerly J. F.: Digital Design. Pronciples and Practices. Prentice Hall, Upper Saddle River, 2000.


2. Zieliński C.: Podstawy projektowania układów cyfrowych. PWN, Warszawa, 2003