Engineering topics
Publications and source records attributed to Bennett, A. W..
The concept of Boolean integration is introduced and developed. When the changes in a desired function are specified in terms of changes in its arguments, then ways of 'integrating' (i.e., realizing) the function, if it exists, are presented. Boolean integral calculus has applications in design of logic circuits.
Algorithms are presented for differentiation and integration of Boolean functions by means of Karnaugh maps. The algorithms are considered simple when the number of variables is six or less; in this case Boolean differentiation and integration is said to be as easy as the Karnaugh map method of simplifying switching functions. It is suggested that the algorithms would be useful in the analysis of faults in combinational systems and in the synthesis of asynchronous sequential systems which utilize edge-sensitive flip-flops.
This paper presents the necessary and sufficient conditions for a given differential expression to be compatibly integrable and it presents the necessary and sufficient conditions for a given expression to be exactly integrable. Methods are given for integrating a differential expression when it is exactly integrable and when it is compatibly integrable. The physical interpretation is given of the integral of order k, of a differential expression, and it is shown that any differential expression of the proper form is integrable by parts.
A transition calculus is presented for analyzing the effect of input changes on the output of logic circuits. The method is closely related to the Boolean difference, but it is more powerful. Both differentiation and integration are considered.