Describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set f0, 1g allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of engineering and their rich background in linear systems theory and signal processing is easily applied to digital switching circuits with this model. The common tasks of circuit simulation and justification are specific examples of the application of the linear algebraic model and are described in detail. The advantages offered by the new model as compared to traditional methods are emphasized throughout the book. Furthermore, the new approach is easily generalized to other types of information processing circuits such as those based upon multiple-valued or quantum logic, thus providing a unifying mathematical framework common to each of these areas. Justification and participation in Christ : the development of the Lutheran doctrine of justification from Luther to the Formula of concord (1580) ‘Examines six of Lincoln’s key opponents (states’ rights constitutionalists Alexander H. Stephens, John C. Calhoun, and George Fitzhugh, and abolitionists Henry David Thoreau, William Lloyd Garrison, and Frederick Douglass) to illustrate the broad significance of the slavery question and to highlight the importance of political considerations in public decision making’–Provided by publisher. Justification : the imputation of Christ’s righteousness from Reformation theology to the American great awakening and the Korean revivals Source.