The following logic gate combination is equiv | vedclass

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

Question

(C) The given circuit consists of an $OR$ gate and a $NAND$ gate whose outputs are fed into an $AND$ gate.Let the inputs be $A$ and $B$.The output of

Vedclass · Accepted Answer

$XOR$ gate

Vedclass · Answer

(C) The given circuit consists of an $OR$ gate and a $NAND$ gate whose outputs are fed into an $AND$ gate.Let the inputs be $A$ and $B$.The output of the $OR$ gate is $(A + B)$.The output of the $NAND$ gate is $(\overline{A \cdot B})$.These are the inputs to the final $AND$ gate.Therefore,the final output $Y$ is given by:$Y = (A + B) \cdot (\overline{A \cdot B})$Using De Morgan's theorem,$\overline{A \cdot B} = \bar{A} + \bar{B}$.$Y = (A + B) \cdot (\bar{A} + \bar{B})$$Y = A \cdot \bar{A} + A \cdot \bar{B} + B \cdot \bar{A} + B \cdot \bar{B}$Since $A \cdot \bar{A} = 0$ and $B \cdot \bar{B} = 0$,we have:$Y = 0 + A \cdot \bar{B} + B \cdot \bar{A} + 0$$Y = A \cdot \bar{B} + \bar{A} \cdot B$This is the Boolean expression for an $XOR$ gate.

Input $A$	Input $B$	Output $Y$
$0$	$1$	$C$
$0$	$0$	$D$
$1$	$0$	$E$
$1$	$1$	$F$

The following logic gate combination is equivalent to

Similar Questions

For the logic circuit shown in the figure,the Boolean expression is:

The following figure $(i)$ shows a logic gate circuit with two inputs $A$ and $B$ and output $C$. The voltage waveforms of $A, B$,and $C$ are as shown in the figure $(ii)$ given below. The logic circuit gate is:

For which of the following Boolean expressions is the result always zero?

Identify the logic operation carried out by the given circuit.

For a $NAND$ gate, the inputs and outputs are given in the table below. The values taken by $C, D, E, F$ are respectively:
Input $A$ Input $B$ Output $Y$
$0$ $1$ $C$
$0$ $0$ $D$
$1$ $0$ $E$
$1$ $1$ $F$

Vedclass Test Series

Exam Paper Generator

Online Exam Module