Write the truth table for a $NAND$ gate connected as given in the figure. Hence,identify the exact logic operation carried out by this circuit.
(N/A) In the given circuit,the input $A$ is connected to both inputs of the $NAND$ gate. Let the inputs be $A_1 = A$ and $A_2 = A$. The output $Y$ of a $NAND$ gate is given by $Y = \overline{A_1 \cdot A_2}$.
Substituting the inputs,we get:
$Y = \overline{A \cdot A}$
Using the Boolean identity $A \cdot A = A$,we have:
$Y = \overline{A}$
The truth table for this operation is:
Since the output $Y$ is the complement of the input $A$,this circuit functions as a $NOT$ gate.
Substituting the inputs,we get:
$Y = \overline{A \cdot A}$
Using the Boolean identity $A \cdot A = A$,we have:
$Y = \overline{A}$
The truth table for this operation is:
| $A$ | $Y = \overline{A}$ |
|---|---|
| $0$ | $1$ |
| $1$ | $0$ |
Since the output $Y$ is the complement of the input $A$,this circuit functions as a $NOT$ gate.
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$(i)$ provide a continuous set of values
(ii) represent values as discrete steps
(iii) can utilise binary system
(iv) are in the form of rectangular waves
Then the true statements are:
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The Boolean expression $Y = A \bar{B} C + \bar{A} \bar{C}$ can be realized with which of the following gate configurations?
$A.$ One $3$-input $\text{AND}$ gate,$2$ $\text{NOT}$ gates,one $2$-input $\text{AND}$ gate,and one $2$-input $\text{OR}$ gate.
$B.$ One $3$-input $\text{AND}$ gate,$2$ $\text{NOT}$ gates,one $2$-input $\text{NAND}$ gate,and one $2$-input $\text{OR}$ gate.
$C.$ One $3$-input $\text{OR}$ gate,$3$ $\text{NOT}$ gates,and one $2$-input $\text{AND}$ gate.
Choose the correct answer from the options given below.
$A.$ One $3$-input $\text{AND}$ gate,$2$ $\text{NOT}$ gates,one $2$-input $\text{AND}$ gate,and one $2$-input $\text{OR}$ gate.
$B.$ One $3$-input $\text{AND}$ gate,$2$ $\text{NOT}$ gates,one $2$-input $\text{NAND}$ gate,and one $2$-input $\text{OR}$ gate.
$C.$ One $3$-input $\text{OR}$ gate,$3$ $\text{NOT}$ gates,and one $2$-input $\text{AND}$ gate.
Choose the correct answer from the options given below.
DifficultJEE MAIN 2025
View SolutionWhich of the following represents the $NAND$ gate?
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