The characteristic equation of D-flip-flop implies that ___________a)The next state is dependent on previous stateb)The next state is dependent on present statec)The next state is independent of previous stated)The next state is independent of present stateCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Characteristics of D-flip-flop:
A D-flip-flop is a sequential logic device that can store one bit of data. It has two inputs - a data input (D) and a clock input (CLK), and two outputs - the output (Q) and its complement (Q'). The D-flip-flop changes its output based on the input data and the clock signal.

Characteristic equation:
The characteristic equation of a D-flip-flop is given by the expression:
Q(t+1) = D

This equation states that the next state of the flip-flop (Q(t+1)) is equal to the input data (D). In other words, the output of the flip-flop at time t+1 is the same as the input at time t.

Explanation:
The given characteristic equation clearly states that the next state of the D-flip-flop is independent of the present state. In other words, the output of the flip-flop at a particular time is solely determined by the input data at that time, and not influenced by the current state of the flip-flop.

This can be understood by considering the behavior of the D-flip-flop. When a clock signal is applied, the input data (D) is sampled and stored in the flip-flop. The stored data becomes the output of the flip-flop until the next clock edge, when a new input data is sampled and stored. Therefore, the output of the flip-flop changes only when the clock signal transitions from one state to another, and the new output is completely determined by the input at that particular instant.

Since the next state of the flip-flop is solely determined by the input data, it is independent of the previous state. The flip-flop does not have any memory or feedback mechanism that would cause the output to depend on the previous state.

Hence, the correct answer is option D - The next state is independent of the present state.

Answer

A characteristic equation is needed when a specific gate requires a specific output in order to satisfy the truth table. The characteristic equation of D flip-flop is given by Q(n+1) = D; which indicates that the next state is independent of the present state.

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