Digital Logic Design: A Rigorous Approach

This introductory textbook, based on the authors’ 15 years experience in teaching logic design, is a complete teaching tool for turning students into logic designers in one semester. It covers combinational circuits, basic computer arithmetic, synchronous circuits, finite state machines, logical simulation, and an implementation of a simple RISC processor and its machine language. Each chapter first describes new concepts and then gives extensive applications and examples of these new ideas. Assuming no prior knowledge of discrete mathematics, the authors introduce all the necessary background in propositional logic, asymptotics, graphs, hardware and electronics. Important features of the presentation are:

• Every designed circuit is formally specified and implemented; the correctness of the implementation is proved, and the cost and delay are analyzed
• Algorithmic solutions are offered for tasks such as logical simulation, computation of propagation delay, and minimum clock period
• Connections are drawn from the physical analog world to the digital abstraction • The language of graphs is used to describe formulas and circuits
• Hundreds of figures, examples and exercises enhance understanding The extensive website http://www.eng.tau.ac.il/~guy/Even-Medina/ includes teaching slides and links to Logisim and a DLX assembly simulator.

Table of Contents

Part I Preliminaries
Chapter 1. Sets and Functions
Chapter 2. Induction and Recursion
Chapter 3. Sequences and Series
Chapter 4. Directed Graphs
Chapter 5. Binary Representation
Chapter 6. Propositional Logic
Chapter 7. Asymptotics
Chapter 8. Computer Stories: Big Endian vs. Little Endian

Part II Combinational Circuits
Chapter 9. Representation by Formulas
Chapter 10. The Digital Abstraction
Chapter 11. Foundations of combinational circuits
Chapter 12. Trees
Chapter 13. Decoders and Encoders
Chapter 14. Selectors and Shifters
Chapter 15. Addition
Chapter 16. Signed Addition

Part III Synchronous Circuits
Chapter 17. Flip-Flops
Chapter 18. Memory Modules
Chapter 19. Foundations of Synchronous Circuits
Chapter 20. Synchronous Modules: Analysis and Synthesis

Part IV A Simplified DLX
Chapter 21. The ISA of a Simplified DLX
Chapter 22. A Simplified DLX: Implementation