Draw the logic circuit diagrams for equations given in part $1$ and $2$ in lab $3$ using only AND, OR$,$ and NOT gates.

In Part $1,$ simplify equation F$1$ using Boolean laws

$($Hint: Following laws can be used:

X $+$ X $=$ X

Consensus theorem

A $=$ AB $+$ AB$\text{'}$

X$\text{'}$Y $+$ X $=$ X $+$ Y

$).$

State each law used. The most simplified solution should have four terms.

The logic diagram should be drawn for the simplified form of the equations.

Derive truth tables for each function.

Part $1$:

F$2=$ ABC'D'

F$1=$ ABC $+$ A'B'C'D' $+$ A'B'D$+$ A'CD' $+$ AB'C' $+$ A'CD $+$ A'B'D

F$0=($A$\text{'}$B$+$AB$\text{'})($CD$+$C$\text{'}$D$\text{'})+($AB $+$A$\text{'}$B$\text{'})($C$\text{'}$D$+$CD$\text{'})$

Part $2$:

F$15=$ WXYZ

F$14=$ WXYZ$\text{'}$

F$13=$ WXY$\text{'}$Z

F$12=$ WXY$\text{'}$Z$\text{'}$

F$11=$ WX$\text{'}$YZ

F$10=$ WX$\text{'}$YZ$\text{'}$

F$9=$ WX$\text{'}$Y$\text{'}$Z

F$8=$ WX$\text{'}$Y$\text{'}$Z$\text{'}$

F$7=$ W$\text{'}$XYZ

F$6=$ W$\text{'}$XYZ$\text{'}$

F$5=$ W$\text{'}$XY$\text{'}$Z

F$4=$ W$\text{'}$XY$\text{'}$Z$\text{'}$

F$3=$ W$\text{'}$X$\text{'}$YZ

F$2=$ W$\text{'}$X$\text{'}$YZ$\text{'}$

F$1=$ W$\text{'}$X$\text{'}$Y$\text{'}$Z

F$0=$ W$\text{'}$X$\text{'}$Y$\text{'}$Z$\text{'}$