Applications of Multidimensional Polynomial Algebra to Bubble Circuits

The operation of bubble circuits depends on the accurate functioning of individual elements such as channeling gates, logic gates, generators, etc., at the critical instants of time. When the circuit becomes complicated, it is not easy to comprehend a multiplicity of functions and determine accurately the instant and duration of operations of these critical elements. Further, a bubble circuit cannot be easily altered like a prototype experimental electrical circuit; and it becomes necessary to ascertain the proper functioning of the designed bubble circuit prior to its actual construction. In this paper the technique developed in Ref. 1 is applied to three circuits, and the operation of each circuit is predicted. In the second example, the design parameters such as the operating time of the gates, their duration, and the overall timing for the circuit, are derived step by step as the algebra progresses.