Design a Mealy type sequential circuit to operate as follows

Design a Mealy type sequential circuit to operate as follows: The machine has one input x and one output z. Let U(T) and V (T) denote the number of 1-inputs and 0-inputs, respectively, to the circuit from t = 0 to T. The output at time T, z(T) should be 1 if and only if V (T) U(T) = 3k for some integer k (i.e. V (T) U(T) = . . . 9, 6, 3, 0, 3, 6, 9, . . .).

(a) Construct the state table.

(b) Derive the circuit assuming JK memory elements.

NOTE: The characteristic equation for a JK is Q(t+1) = J(t)Q(t)+K(t)Q(t).

The transition table is as follows:

0 0 : J = 0, K = , 0 1 : J = 1, K = , 1 0 : J = , K = 1, 1 1 : J = , K = 0.

Solution

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