Banach lattices and operators by Schwarz H.-U.

By Schwarz H.-U.

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Example text

For example, in the state transition a 2a1a 0 = 000 a 2+ a1+ a 0+ = 001, applying Q+(next state) yields: a +2 = J 2 Q 2 (t ) + K 2 Q 2 (t ) = a1a 0 a 2 + a1a 0 a 2 . Thus, a +2 = a1a 0 a 2 + a1a 0 a 2 = 001 + 000 = 0, a1+ = J1 Q1 (t) + K1Q1 (t) = a 0 a1 + a 0 a1 .

23, to see whether there are any redundant states. If there are, the reduction in states is reflected in the revised state sequence table. 45, state Z is identified as being redundant because the next state for both states V and Z is W, and the state changes have the same inputs and outputs (1, 1). 23 State diagram for minimization of states. 45. 45 is Y because both Y and W have the next state V, with same state change inputs and outputs (1, 0). 45. 46. 24 shows the result of eliminating redundant states in the state diagram.

38 when T = 1, the input Q(t) is toggled, producing its complement in output Q(t + 1). 19, at the Q output, we see that: Q(t + 1) = TQ(t ) + T Q(t ) = (TQ(t ))(T Q(t )) = (T + Q(t ))(T + Q(t )) = T Q(t ) + T Q(t ). Furthermore, the equation for Q(t +1) is derived as follows: Q(t + 1) = T Q(t ) + T Q(t ) = (T Q(t ))(T Q(t )) = (T + Q(t ))(T + Q(t )) = T Q(t ) + T Q(t ). 19 feedback from the flip-flop outputs to the inputs is used to obtain the desired outputs at time t + 1. Problem: Based on the above equations, develop the T flip-flop truth table.

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