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JK flip-flop is the modified version of SR flip-flop. It operates with only positive clock transitions or negative clock transitions. The circuit diagram of JK flip-flop is shown in the following figure.
This circuit has two inputs J & K and two outputs Q(t) & Q(t)’. The operation of JK flip-flop is similar to SR flip-flop. Here, the inputs of SR flip-flop are considered as S = J Q(t)’ and R = KQ(t) in order to utilize the modified SR flip-flop for 4 combinations of inputs.
Here, Q(t) & Q(t + 1) are present state & next state respectively. So, JK flip-flop can be used for one of these four functions such as Hold, Reset, Set & Complement of present state based on the input conditions, when positive transition of clock signal is applied.
By using three variable K-Map, you can get the simplified expression for next state, Q(t + 1). The three variable K-Map for next state, Q(t + 1) is shown in the following figure.
The maximum possible groupings of adjacent ones are already shown in the figure. Therefore, the simplified expression for next state Q(t+1) is
Q(t + 1) = J.Q(t)' + K'.Q(t)