Modern digital circuits, especially those based on large-scale integration devices employ DE flip flops, which are an extension of the D type with the capacity to store an input value only upon request or enabling. The DE flip flop could possibly be described algebraically by its characteristic equation or tabularly by its next-state table (used for analysis purposes) and its excitation table (used for synthesis purposes). This paper explores two novel characterizations of DE flip flops. First, equational and implicational descriptions are presented, and the Modern Syllogistic Method is utilized to produce complete statements of all propositions that are true for a general DE 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 plays a crucial role in exposing the pertinent concepts and implementing the various desired derivations. This paper is expected to be of an immediate pedagogical benefit, and to facilitate the analysis and synthesis of contemporary sequential digital circuits.