Instructions

$-$ If all steps are not shown in detail, no credit will be granted for the correct final solutions.

$-$ Please use blank sheets of paper to neatly write your solutions, do not write answers in the spaces between the questions.

$1)$ Analyze the following ripple counters and check whether the counter is counting up or counting down by drawing the timing diagram. Show the timing diagram for $10$ count pulses. Assume the initial values of the flip flops are reset to $0.$

a$)[5$ pts$]$ Note that the LSB is O A and MSB is On $.$ As usual LSB receives the count pulse.

b$)[5$ pts$]$ Note that the LSB is Qo and MSB is Q$2.$ As usual LSB receives the count pulse.

Question $2[25$ pts$]$

Design a synchronous counter using JK flip flops that gocs through the sequence $\backslash (2\backslash$Rightarrow $6\backslash$sim $1\backslash$sim $7\backslash$sim $5\backslash )$ 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.