A binary variable Z is defined by the truth table shown.

Which expression corresponds to the fundamental product

for Z$?$

aZ$()/($b$)=$ar $($A$)($B$)/($b$)$ar $($C$)(+)/($b$)$ar $($A$)$BC$+$A$($B$)/($b$)$ar $($C$)+$ABC

bZ$()/($b$)=$ar $($A$)/($b$)$ar $($B$)/($b$)$ar $($C$)(+)/($b$)$ar $($A$)/($b$)$ar $($B$)$C$+($A$)/($b$)$ar $($B$)/($b$)$ar $($C$)+($A$)/($b$)$ar $($B$)$C

cZ$=($A$+$B$+$C$)*($A$+$B$(+)/($b$)$ar $($C$))*(()/($bar$)($A$)+$B$+$C$)*(()/($bar$)($A$)+$B$(+)/($b$)$ar $($C$))$

dZ$=($A$(+)/($b$)$ar $($B$)+$C$)*($A$(+)/($b$)$ar $($B$)(+)/($b$)$ar $($C$))*(()/($bar$)($A$)(+)/($b$)$ar $($B$)+$C$)*(()/($bar$)($A$)(+)/($b$)$ar $($B$)(+)/($b$)$ar $($C$))$

a

A Karnaugh Map is shown below. Which function is the

correct minimum sum derived from the Karnaugh Map?

aZ$()/($b$)=$ar $($A$)($B$)/($b$)$ar $($C$)+$A$($B$)/($b$)$ar $($C$)(+)/($b$)$ar $($A$)/($b$)$ar $($C$)$D

bZ$=($B$)/($b$)$ar $($C$)(+)/($b$)$ar $($A$)/($b$)$ar $($C$)$D

cZ$()/($b$)=$ar $($A$)(+)/($b$)$ar $($C$)$

dZ$()/($b$)=$ar $($C$)$D$+$B

Karnaugh Map

a

The function Z below is to be implemented using an

integrated circuit that contains only NAND gates. Use

DeMorgan's laws to convert it to a form using only NAND

gates $($and inverters$).$ Which function aZ$=($A$)/($b$)$ar $($B$)$C$(+)/($b$)$ar $($A$)($B$)/($b$)$ar $($C$)(+)/($b$)$ar $($A$)/($b$)$ar $($B$)/($b$)$ar $($C$)$

aZ$()/($b$)=$ar $(()/($bar$)(($A$)/($b$)$ar $($B$)$C$))+(()/($bar$)(()/($bar$)($A$)$B$)/($b$)$ar $($C$))+(()/($bar$)(()/($bar$)($A$)/($b$)$ar $(()/($bar$)($B$))/($b$)$ar $($C$)))$

bZ$=(()/($bar$)(()/($bar$)($A$)+$B$(+)/($b$)$ar $($C$)))+($A$(+)/($b$)$ar $($B$)+$C$)+(()/($bar$)($A$+$B$+$C$))$

cZ$()/($b$)=$ar $(()/($bar$)(()/($bar$)($AB$)/($b$)$ar $($C$)))*(()/($bar$)(($A$)/($b$)$ar $($B$)$C$))(*)/($b$)$ar $(($ABC$))$

dZ$()/($b$)=$ar $(()/($bar$)(($A$)/($b$)$ar $($B$)$C$))*(()/($bar$)(()/($bar$)($A$)($B$)/($b$)$ar $($C$)))*(()/($bar$)(()/($bar$)($A$)/($b$)$ar $($B$)/($b$)$ar $($C$)))$

$\_($a$)$

b