It is required to design a binary mod-5 synchronus counter using AB flip-flops such that the output Q₂Q₁Q₀ changes as $$000 \to 001 \to 010$$ ........and so on. The excitation table for the AB flip-flops is given in the table

(a) Write down the state table for the mod-5 counter.
(b)Obtain simplified SOP expressions for the inputs A₂, B₂, A₁, B₁, A₀ and B₀ in terms of Q₂, Q₁, Q and their complements.
(c) Hence, complete the circuit diagram for the mod-5 counter given in the figure using minimum number of 2-input NAND-gate only.

The circuit diagram of a synchronous counter is shown in the figure. Determine the sequence of states of the counter assuming that the initial state is ‘000’. Give your answer in a tabulor form showing the present state Q_A(n), Q_B(n), Q_C(n), J-K inputs ( J_A, K_A, J_B, K_B, J_C, K,) and the next state $${Q_{A\left( {n + 1} \right)}},\,{Q_{B\left( {n + 1} \right)}},{Q_{C\left( {n + 1} \right)}}$$ From the table, determine the modulus of the counter.

The mod-5 counter shown in figure counts through states Q₂ Q₁ Q₀ = 000, 001, 010, 011 and 100.

(a) Will the counter lockout if it happens to be in any one of the unused states?

(b) Find the maximum rate at which the counter will operate satisfactorily. Assume the propagation delays of flip-flop and AND gate to be t_F and t_A

A sequence generator is shown in figure. The counter status (Q₀ Q₁ Q₃) is intialized to 010 using preset/clear inputs.
The Clock has a period of 50ns and transitions take place at the rising clock edge.
(a) Give the sequence generated at Q₀ till it repeats.
(b) What is the repetition rate for the generated sequence?