(Solved): A- Derive the characteristic equation for the positive edge-triggered JK flip-flop shown below in t ...

Expert Answer

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The positive edge-triggered JK flip-flop is represented in the figure as a block with inputs J, K, and a clock signal C, and outputs Q and Q'.

To derive the characteristic equation, let's define the following variables:

Q(t) - the current state of the flip-flop (output Q) at time t. Q(t+1) - the next state of the flip-flop (output Q) at time t+1. J - the input J of the flip-flop. K - the input K of the flip-flop. C - the clock signal input.

The characteristic equation expresses the next state of the flip-flop (Q(t+1)) in terms of the current state (Q(t)), the inputs (J and K), and the clock signal (C).
In this case, the positive edge-triggered JK flip-flop operates as follows:


1. When the clock signal C transitions from low to high (positive edge), the flip-flop is triggered and its outputs Q and Q' change based on the inputs J and K.

2.If J=0 and K=0, both inputs are inactive, and the flip-flop maintains its current state: Q(t+1) = Q(t)

3.If J=0 and K=1, the flip-flop is in the reset mode, and the output Q is forced to be 0: Q(t+1) = 0

4.If J=1 and K=0, the flip-flop is in the set mode, and the output Q is forced to be 1: Q(t+1) = 1

5.If J=1 and K=1, the flip-flop is in the toggle mode. The output Q toggles to its complemented state: Q(t+1) = ~Q(t)



Combining these conditions, we can write the characteristic equation for the positive edge-triggered JK flip-flop as:

Q(t+1) = JQ'(t) + ~KQ(t)

where Q'(t) represents the complement (negation) of Q(t).

Please note that this characteristic equation assumes ideal behavior and may vary based on specific implementations and edge cases.