In the given network of AND and OR gates, the | vedclass

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(D) Let us trace the output of the logic gates step by step.Step $1$: The first $AND$ gate takes inputs $X_0$ and $X_1$, giving output $Y_1 = X_0 X_1$

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$X_0 X_1 \ldots X_{n-1}+X_2 X_3 X_5 \ldots X_{n-1}+X_{n-2} X_{n-1}+X_n$

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(D) Let us trace the output of the logic gates step by step.Step $1$: The first $AND$ gate takes inputs $X_0$ and $X_1$, giving output $Y_1 = X_0 X_1$.Step $2$: The first $OR$ gate takes $Y_1$ and $X_2$, giving output $Y_2 = X_0 X_1 + X_2$.Step $3$: The next $AND$ gate takes $Y_2$ and $X_3$, giving output $Y_3 = (X_0 X_1 + X_2) X_3 = X_0 X_1 X_3 + X_2 X_3$.Step $4$: The next $OR$ gate takes $Y_3$ and $X_4$, giving output $Y_4 = X_0 X_1 X_3 + X_2 X_3 + X_4$.Continuing this pattern, for an even $n$, the final output $Q$ will be of the form: $Q = X_0 X_1 X_3 X_5 \ldots X_{n-1} + X_2 X_3 X_5 \ldots X_{n-1} + X_4 X_5 \ldots X_{n-1} + \ldots + X_{n-2} X_{n-1} + X_n$.

$A$	$B$	$Y$
$1$	$1$	$0$
$0$	$1$	$1$
$1$	$0$	$1$
$0$	$0$	$1$

In the given network of $AND$ and $OR$ gates, the output $Q$ can be written as (assuming $n$ is even):

Similar Questions

The truth table shown below is for which logic gate?
$A: 0, 0, 1, 1$
$B: 0, 1, 0, 1$
$Y: 1, 0, 0, 1$

Which logic gate is represented by the following truth table?

$A$ $B$ $Y$

$1$ $1$ $0$

$0$ $1$ $1$

$1$ $0$ $1$

$0$ $0$ $1$

The logic gate combination shown in the figure represents which of the following gates?

The input waveforms for the given circuit are shown. Which of the following output waveforms is correct?

Justify the output waveform $(Y)$ of the $OR$ gate for the following inputs $A$ and $B$ given in the figure.

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