The resultant gate and its Boolean expression | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The given circuit consists of two $NOT$ gates ($G_1$ and $G_2$) and one $NOR$ gate $(G_3)$.$1$. The input $A$ passes through the $NOT$ gate $G_1$,

Vedclass · Accepted Answer

$AND, A \cdot B$

Vedclass · Answer

(D) The given circuit consists of two $NOT$ gates ($G_1$ and $G_2$) and one $NOR$ gate $(G_3)$.$1$. The input $A$ passes through the $NOT$ gate $G_1$,so the output at $C$ is $C = \overline{A}$.$2$. The input $B$ passes through the $NOT$ gate $G_2$,so the output at $D$ is $D = \overline{B}$.$3$. These outputs $C$ and $D$ are fed into the $NOR$ gate $G_3$. The output $Y$ of a $NOR$ gate is the complement of the $OR$ of its inputs.$4$. Therefore,$Y = \overline{C + D}$.$5$. Substituting the values of $C$ and $D$,we get $Y = \overline{\overline{A} + \overline{B}}$.$6$. According to De Morgan's theorem,$\overline{\overline{A} + \overline{B}} = \overline{\overline{A}} \cdot \overline{\overline{B}} = A \cdot B$.$7$. The Boolean expression $Y = A \cdot B$ represents an $AND$ gate.Thus,the resultant gate is an $AND$ gate with the expression $A \cdot B$.

The resultant gate and its Boolean expression for the given circuit is

Similar Questions

Four logic gate symbols are given below. Which of these are the symbols for $OR$,$NOR$,and $NAND$ gates,respectively?

The Boolean expression for the following combination is

Which logic gate is represented by the following truth table?
$A$ $B$ $Y$
$0$ $0$ $0$
$0$ $1$ $1$
$1$ $0$ $1$
$1$ $1$ $1$

The real-time variation of input signals $A$ and $B$ are as shown below. If the inputs are fed into a $NAND$ gate,then select the output signal from the following.

If $X$ and $Y$ are the inputs, the given circuit works as . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module