$1-$simplify $F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(0,8,10,12,14)d(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(2,13,15)$

$2-$Using two $38$ decoders and two gates, implement. $F(A,B,C,D)={\displaystyle \underset{?}{\overset{?}{}}}(0,8,10,12,14).$

$3-$ Write a Java function whose input arguments are two bool arrays $a[4]$ and $b[4].$ The

function must interpret these arrays as two $4$ bit numbers, and add them using logical

operators. The results should be in another bool array.

$4-$ Design a two to four bit decoder using only gates.

$5-$ A sequential circuit with two $D$ flip$-$flops A and $B,$ two inputs, $x$ and $y$; and one output $z$

is specified by the following next$-$state and output equations:

$A(t+1)=x{y}_{-}+xB=x{y}^{\text{'}}+xB$

$B(t+1)=xA+x{B}_{-}=xA+x{B}^{\text{'}}$

$z=A$

$($a$)(5)$Draw the logic diagram of the circuit.

$($b$)(10)$List the state table for the sequential circuit.

$($c$)(10)$ Draw the corresponding state diagram.

$6-$ For the following state table

Next State Output

$($a$)$ Tabulate the reduced state table.

$($b$)$ Draw the state diagram corresponding to the reduced state table.

$($c$)$ Implement the circuit using D flip$-$flops