$($a$)$ How a Toggle flip$-$flop can be constructed by using a JK flip$-$flop and

some logic gates. Draw the complete diagram of the circuit.

$(4$ marks$)$

$($b$)$ Design and draw a sequential circuit using D$-$type flip$-$flops that

produce a $15MHz$ frequency signal with $50\%$ duty cycle from a $60MHz$

clock signal with $25\%$ duty cycle. Draw the input and output of your

circuit for a few clock cycles.

$(7$ marks$)$

$($c$)$ Develop and draw a sequential circuit that converts an $8-$bit binary

number to $2\text{'}$s complement form. Assume that the input binary

number is loaded in an $8-$bit shift register. After eight clock cycles, the

shift register has the converted binary number. You can use a suitable

type Flip$-$Flop with some logic gates.

$(14$ marks$)$