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.

Two Novel Characterizations of the DE Flip Flop

“…We recall that the DE flip flop is a variation of the D flip flop, which is simply a D flip flop that is equipped with an enable input E [1,[9][10][11][12] . Despite the contemporary widespread use of the flip flop, it is definitely less familiar (to most readers) than the flip flop.…”

“… The excitations of a flip-flop can be made independent of its present state by setting them as the Boolean quotients (See Appendix A) [1] (…”

“…An essential building block of a sequential digital circuit is an elementary memory cell called a flip flop, a one-bit register, a bistable or a bistable multivibrator [1] . A flip-flop is a circuit that has two stable states and can be used to store a single bit (binary digit) of data; with one of the two states of the flip flop representing a "one" and the other representing a "zero".…”

“…Out of these, we single out the flip-flop as a very versatile device that was commonly used to construct circuits with discrete components. The flip flop is discussed in many publications on digital design (See, e.g., [1][2][3][4][5][6][7][8] ) and its various characterizations are detailed in [1] . However, it has been mostly replaced by a variation of the flip flop, which is conveniently called the flip flop (or occasionally, the E-type flip flop) [1,[9][10][11][12] .…”

“…The flip flop is discussed in many publications on digital design (See, e.g., [1][2][3][4][5][6][7][8] ) and its various characterizations are detailed in [1] . However, it has been mostly replaced by a variation of the flip flop, which is conveniently called the flip flop (or occasionally, the E-type flip flop) [1,[9][10][11][12] . This variation is simply a flip flop that is equipped with an enable input .…”