a$.$ Build a $4$ bit binary synchronous counter using $T$ Flip$-$Flops $(2$ pts$).$

b$.$ Modify the counter in $($a$)$ to design an odd counter that goes through the following

sequences of binary states: $1,3,5,7,9,11,13,15$ and back to $1$ to repeat. Note that

even binary states $0,2,4,6,8,10,12$ and $14$ are not used. The counter must be

self$-$starting; that is$,$ if the circuit starts from any one of the invalid states, the count

pulses must transfer the circuit to the next valid state to continue the count correctly.

i$.$ Draw the state diagram

ii$.$ Derive the state table

iii. Derive the input $FF$ equations

iv$.$ Draw the counter circuit

Question $3(8$ points$)-$ Sequential circuit design with Flip Flop

Given the following state diagram. We want to implement the equivalent circuit using JK$-$FF$.$

a$.$ Define the variables of the problem $($input$,$ output and states$)(1$ pt$)$

b$.$ Derive the state table $(2$ pts$)$

c$.$ Derive the JK$-$FF input equations $(2pts)$

d$.$ Derive the output boolean expression $(1$ pt$)$

e$.$ Draw the sequential circuit of the system $(2$ pts$)$