$($a$)$ Construct a D$-$type flip$-$flop by using a JK flip$-$flop and minimum

number of logic gates. Draw a diagram of the D$-$type flip$-$flop.

$(5$ marks$)$

$($b$)$ If a digital system has $5$ inputs, how many possible input

combinations are there?

Question No$.3$ continues on Page $3$

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$($c$)$ If $A=0,B=1,$ and $C=1$; find $x$ where $x=(Ao+B{)}^{\text{'}}.C$

$($d$)$ Synthesize the following sequential circuit of Figure Q$2$ and

describe the operation of the circuit. Identify the main function of

this circuit by providing an example, where the $8-$bit shift register

is loaded with $(11001110{)}_2$ and the $J-K$ flip$-$flop is cleared.

Determine the content of the shift register after $8$ clock cycles have

been applied. You may ignore any propagation delay.