Mathematical Foundations of Flip-Flops

Abstract : The main purpose of the paper is to lay a mathematical basis for the study of flip-flops. A J-K flip-flop is a device with 2 inputs (zero or one) and two outputs, one of which is always the complement of the other. A counter is a set of J-K flip-flops whose inputs are either constants (0 or 1) or outputs of other flip-flops in the counter. The paper only considers J-K flip-flops whose inputs are outputs of the other flip-flops. Whenever an n-counter is referred to, it shall mean such a counter with no constant inputs. The specification of the connections is called connection list.