Q$1)[8$ points$]$ Using $3$ bit comparators and any required digital components, design a

circuit that compares three numbers. Each number is $3$bits. The largest number will be

displayed on $7$ segment display. $($use block diagrams of the comparators$)$

Q$2)[8$ points$]$ Using JK flip flops, design a counter that counts $0-2-4-6$ and back to zero

if the input is $1.$ And it will count $0-6-4-2$ and back to $0$ if the input is $0.$ The count will be

displayed on $7$ segment display.

Q$3)[9$ points$]$ The bank uses a queue system to ensure the privacy of its customers.

Each customer gets a number and waits for his$/$her turn.

Each teller $()$ announces the customer number which will be serviced using two

seven$-$segment displays: one to show the customer's number and the other to show the

teller's desk number.

Each teller has

$1-$ a push button to call the next customer

$2-$ A seven$-$segment display to display the customer number.

$3-$ A unique desk number

The system has

$1-$ A counter

$2-$ push buttons

$3-$ One main seven$-$segment display to show the customer's number

$4-$ One main seven$-$segment display to show the teller's number

$5-$ One seven$-$segment display for each teller to show the customer's number.

When a teller presses the push button

The counter increases by one

The content of the counter is displayed on the teller $7-$segment display.

The content of the counter is displayed on the main $7-$segment display

The teller number who pressed the button is displayed on the main $7-$segment

display associated with the teller desk number

Suppose the bank has $3$ tellers, the customers' numbers are from $0-9$

you have $5$ Seven$-$segment displays and one counter.

Use a block diagram in your design

Show the gate$-$level design for the counter.