Two Novel Characterizations of the DE Flip Flop

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.