Novel Characterizations of the JK Bistables (Flip Flops)

Abstract

The JK flip flop is a flexible type of bistable elements that has extensive uses in digital electronics and control circuits. It is usually described by its characteristic equation or next-state table (used for analysis purposes) and its excitation table (used for synthesis purposes). This paper explores a variety of novel characterizations of JK flip flops. First, equational and implicational descriptions are presented, and methods of logic deduction are utilized to produce complete statements of all propositions that are true for a general JK flip flop. Next, methods of Boolean-equation solving are employed to find all possible ways to express the excitations in terms of the present state and next state. The concept of Boolean quotient is used to impose certain requirements so as to find particularly useful expressions of the excitations. Relations of JK flip flops to other types of flip flops are also explored. This paper is expected to provide an immediate pedagogical benefit, and to help facilitate the analysis and synthesis of sequential digital circuits.