Question

Whaqt will be the output of given logical circuit

• A. $\stackrel{-}{A}.B$
• B. $A.B$ + $\stackrel{-}{A.}\stackrel{-}{B}$
• C. $\stackrel{-}{A.}B$ + $A.\stackrel{-}{B}$
• D. $A.\stackrel{-}{B}$

Answer 1

Answer: (D)

$A.\stackrel{-}{B}$

To solve this question, we will need De Morgan’s laws (or Theorems):

$\left(i\right)\overline{A+B}=\overline{A}\cdot \overline{B}$

$\left(ii\right)\overline{A\cdot B}=\overline{A}+\overline{B}$

$\left(iii\right)\overline{\overline{A}+\overline{B}}=A\cdot B$

$\left(iv\right)\overline{\overline{A}\cdot \overline{B}}=A+B$

The output is calculated as per the image by using De Morgan's laws mentioned above:

$Y=\overline{\left(\overline{A}+AB\right)\cdot (\overline{AB}+B})$

$⟹Y=\overline{\left(\overline{A}+AB\right)}+\overline{(\overline{AB}+B})$

$⟹Y=(A\cdot \overline{AB})+(AB\cdot \overline{B})$

$⟹Y=A(\overline{A}+\overline{B})+0$ (As $X\cdot \overline{X}=0$)

$⟹Y=0+A\overline{B}$

$⟹Y=A\overline{B}$

So the correct answer is option (D) $A\overline{B}$