Logical Instruments for Teaching Logical Design

A way of teaching combinatorial logic is presently based on experimentation with physical models of logical relations ("logical instruments"). The Marquand chart [7] originated in 1881 is described and discussed. A graphical representation of a Boolean function on that chart is processed by experimental application of "implication masks." As an example of such a processing, the paper describes the construction of a minimal Σπ-form of a given Boolean function (by respecting DON'T-CARE conditions). The main part of the minimization algorithm is based on a sufficient condition of extension (of the expression (9) towards the minimal), which is satisfied if a certain "necessary condition of extension" does hold and if a certain "sufficient condition of exclusion" does not. To save processing time, a weight is assigned to each point on the chart where the Boolean function must be 1 (true). Then the minimization algorithm is applied, with a preference to points with smaller weights. Logical punch cards are used as a logical instrument for experimental evaluation of weights.