By Guy Even

This introductory textbook, in keeping with the authors' 15 years event in educating common sense layout, is an entire educating device for turning scholars into good judgment designers in a single semester. It covers combinational circuits, easy machine mathematics, synchronous circuits, finite country machines, logical simulation, and an implementation of an easy RISC processor and its computer language. every one bankruptcy first describes new ideas after which offers broad functions and examples of those new principles. Assuming no earlier wisdom of discrete arithmetic, the authors introduce all of the worthy history in propositional common sense, asymptotics, graphs, and electronics. very important beneficial properties of the presentation are: • each designed circuit is officially special and carried out; the correctness of the implementation is proved, and the fee and hold up are analyzed • Algorithmic ideas are provided for initiatives equivalent to logical simulation, computation of propagation hold up, and minimal clock interval • Connections are drawn from the actual analog global to the electronic abstraction • The language of graphs is used to explain formulation and circuits • countless numbers of figures, examples and workouts improve knowing The vast site http://www.eng.tau.ac.il/~guy/Even-Medina/ comprises instructing slides and hyperlinks to Logisim and a DLX meeting simulator.

Show description

Read Online or Download Digital Logic Design: A Rigorous Approach PDF

Best logic books

Errors of Reasoning. Naturalizing the Logic of Inference

Blunders of Reasoning is the long-awaited continuation of the author's research of the good judgment of cognitive structures. the current concentration is the person human reasoner working less than the stipulations and pressures of genuine existence with capacities and assets the wildlife makes to be had to him.

The Is-Ought Problem: An Investigation in Philosophical Logic

Can OUGHT be derived from IS? This booklet provides an research of this commonly used challenge through alethic-deontic predicate common sense. New during this research is the leitmotif of relevance: is-ought inferences certainly exist, yet they're all beside the point in an exact logical experience. New evidence concepts identify this end result for extraordinarily vast periods of logics.

Functional and Logic Programming: 5th International Symposium, FLOPS 2001 Tokyo, Japan, March 7–9, 2001 Proceedings

This e-book constitutes the refereed court cases of the fifth overseas Symposium on practical and common sense Programming, FLOPS 2001, held in Tokyo, Japan in March 2001. The 21 revised complete papers provided including 3 invited papers have been conscientiously reviewed and chosen from forty submissions. The publication bargains topical sections on sensible programming, good judgment programming, practical common sense programming, kinds, software research and transformation, and Lambda calculus.

Extra info for Digital Logic Design: A Rigorous Approach

Example text

By definition this means that ∀x ∈ U ∶ x ∈ A ⇒ x ∈ B . 1) 8 CHAPTER 1. 1: Venn diagrams over the sets A and B with respect to the universal set U. ¯ ⊆ A. ¯ For the sake of contradiction, assume that there Now we wish to show that B ¯ and x ∈/ A. ¯ This means that x ∈/ B and x ∈ A. exists an element x for which x ∈ B ¯ ¯ But this contradicts Eq. 1. Hence, B ⊆ A, as required. ¯ Note that A¯ = A ¯ ⊆ A. ¯ By the proof above, it follows that A¯ ⊆ B. Assume that B ¯ and B = B. Hence, A ⊆ B, as required.

Indeed, b′ = f (a′ ), and b′ is unique, as required. Now, we prove that the function g ∶ A′ → B ′ is onto; namely, for every b′ ∈ B ′ , there exists an a′ ∈ A′ such that f (a′ ) = b′ . The proof is as follows. Let b′ ∈ B ′ . Since B ′ ⊆ B, then b′ ∈ B. Since f ∶ A → B is onto, there exists an a′ ∈ A such that f (a′ ) = b′ . To complete the proof, it suffices to show that a′ ∈ A′ . Indeed, a′ ∈/ f −1 (B ∖ B ′ ). It follows that a′ ∈ A′ , and the lemma follows. 3. 4. 3 Prove the following theorem.

The idea is to depict each set as a region defined by a closed curve in the plane. For example, a set can be depicted by a disk. Elements in the set are represented by points in the disk, and elements not in the set are represented by points outside the disk. The intersections between regions partition the planes into “cells”, where each cell represents an intersection of sets and complements of sets. 1, we depict the union, intersection, difference and complement of two sets A and B that are subsets of a universal set U.

Download PDF sample

Rated 4.59 of 5 – based on 30 votes