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Master-Slave JK Flip-Flop

A fundamental memory element that uses two cascaded latches (master and slave) to ensure that the output only changes on the active edge of the clock signal, preventing race conditions.

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The statement of the theorem

The JK flip-flop uses two cascaded latches (Master and Slave) controlled by a clock signal

\text{CLK}

. The Master latch captures the input

J

and

K

when

\text{CLK}=1

. The Slave latch updates the output

Q_{next}

when

\text{CLK}

transitions from 1 to 0. The next state

Q_{next}

is governed by the input

J

and

K

and the current state

Q

Q_{next} = J \overline{Q} + \overline{K} Q

This structure ensures that the output only changes on the active edge of the clock signal.