Using T flip flops, we want to design a cyclic counter which has an output sequence of period 6 as shown: 000 001 011 111 110 100 000 001 ... The counter does not have an input signal, but moves to the appropriate next state at every clock. Code the states so that the output at each state will be the same as the state assignment, in other words, z(t) = s(t) ( z(t), s(t) are output and state assignment at time t respectively). Assume that the counter will always start at 000 and will never enter an unused state.

a) (4 Points) Draw the state diagram for this system

b) (6 Points) Show the state transition table

c) (6 Points) Draw the K-maps for each T (input of T flip-flops)

d) (6 Points) Write switching expressions for each T (input of T flip-flops)

e) (6 Points) Draw your gate level design (using gates and T flip-flops)