Switching Machines: Volume 1: Combinational Systems by J.-P. Perrin, M. Denouette, E. Daclin (auth.)

By J.-P. Perrin, M. Denouette, E. Daclin (auth.)

We shall start this short part with what we deliberate to be its aim. it will likely be through the most define after which concluded via a number of notes as to how this paintings could be used. even though logical structures were synthetic for it slow, the speculation at the back of them is kind of fresh. with out going into historic digressions, we easily comment that the 1st accomplished principles at the software of Boolean algebra to logical platforms seemed within the 1930's. those structures seemed in phone exchanges and have been learned with relays. it's only round 1955 that many articles and books attempting to systematize the learn of such automata, seemed. in view that then, the speculation has complex usually, yet now not in a fashion which satisfies these interested in useful functions. what's critical, is that apart the books through Caldwell (which dates already from 1958), Marcus, and P. Naslin (in France), few works were released which try and assemble and unify effects which are utilized by the practis­ ing engineer; this is often the target of the current volumes.

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Extra info for Switching Machines: Volume 1: Combinational Systems Introduction to Sequential Systems

Example text

We can thus write function F in the form of G but we must make sure that the functions cp are appropriate. 3 stating that the columns of E' are distinct, if two columns i and j of matrix E are identical, columns i andj of matrix [T] must be also identical. If conditions (a) and (b) are satisfied the decomposition of function F with the help of functions

The study of Boolean function factorization (or decomposition) has been developing for some years. In the following we shall expose the principal results obtained at the present time. Before discussing the Boolean factorization theory itself, we must have some notion of Boolean matrices, which are the subject of the next section. After defining two principal types of problems, we shall apply ourselves to the task of solving them. Limiting ourselves to a brief review, we shall expose the theoretical concepts necessary to understand factorization.

When the function is given by simple transcription of its designation number (as the Boolean sum of Boolean products of variables), its form is unique; we call it the disjunctive canonical form off If it is a function of n variables, each of its terms is a Boolean product ofthe n variables, some of which are barred and others non-barred. These Boolean products are called minterms of the disjunctive canonical form. Several disjunctive reduced forms obtained by simplification correspond to the same disjunctive canonical form.

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