Section 4.2: Flip-flops From the SR flip-flop truth table, the unused state where S and R are both true is wasted. The JK flip-flop patented by Eldred Nelson in 1953 uses this unused state to toggle the output. J works like S in the and K works like R in the SR flip-flop. We can rewrite the truth table. J |[K ]1Q [QF —1J Q[ Out K Q G X.0 A\ CLK X, 0 JK = (OO0 RN X | a|lOl0Om|~O|O = O|=1O|=O0|— |0 OO0 O Figure 4.2.0: JK Flip-flop Truth Table, Symbol, and State Diagram When J and K are both true the state Q toggles, so that the next state Q* is the compliment of Q. The JK flip-flop works similar to the SR flip-flop. The output Q changes on the clock edge. The state diagram shows that if the state of Q is 0 and J is 1, the next value of Q on the clock edge is 1. At that point K true results in a next state of of Q being 0 on the clock edge. Remember J sets the next state to 1, and K sets the next state to 0. If both are 1 (true) then the state of Q toggles from 0 to 1 or 1 to 0. This toggle is the difference between the JK flipflop and the SR flipflop. This allows us to make any flipflop action with a JK flipflop, so it is often referred to as the Universal Flipflop. Summing the minterms from this truth table Q* = JK'Q" + JKQ' + J’K'Q + JK'Q. As expression a cononical sum (contains only minterms), it can be simplified fully using the adjacency property. Simplfying JK'Q’ + JKQ' = JQ' and J'K'Q + JK'Q = K'Q. So the equation for the JK flip-flop is Q* = JQ' +
