Question $2[25$ pts$]$

Design a synchronous counter using JK flip flops that goes through the sequence $26->175$ and repeat. $($Hint: there are unused states which must be considered as don't cares.$)$

a$)$ Obtain the state table showing present states, next states and flip flop inputs.

b$)$ Draw k$-$maps and obtain flip flop input equations.

c$)$ Draw the circuit diagram. Properly label the flip flop inputs and outputs.

d$)$ What happens if the circuit goes to one of the unused states? Show your method of analysis.

e$)$ Show a state diagram, including the unused states.