# Current Affairs JEE Main & Advanced

## Logic Gates

Category : JEE Main & Advanced

(i) AND : It is the boolean function defined by

$f({{x}_{1}},{{x}_{2}})={{x}_{1}}\wedge {{x}_{2}}$; ${{x}_{1}},\,{{x}_{2}}\in \{0,\,1\}$.

It is shown in the figure given below.

 Input Output ${{x}_{1}}$ ${{x}_{2}}$ ${{x}_{1}}\wedge {{x}_{2}}$ 1 1 0 0 1 0 1 0 1 0 0 0

(ii) OR : It is the boolean function defined by

$f({{x}_{1}},{{x}_{2}})={{x}_{1}}\vee {{x}_{2}}$; ${{x}_{1}},{{x}_{2}}\in \{0,\,1\}$.

It is shown in the figure given below

 Input Output ${{x}_{1}}$ ${{x}_{2}}$ ${{x}_{1}}\vee {{x}_{2}}$ 1 1 0 0 1 0 1 0 1 1 1 0

(iii) NOT : It is the boolean function defined by

$f(x)={x}',$ $x\in \{0.1\}$

It is shown in the figure given below:

 Input Output x 1 0 x¢ 0 1

Combinational circuit :

In the above figure, output s in uniquely defined for each combination of inputs ${{x}_{1}},{{x}_{2}}$ and ${{x}_{3}}$. Such a circuit is called a combinatorial circuit or combinational circuit.

In the above figure, if ${{x}_{1}}=1,{{x}_{2}}=0$, then the inputs to the AND gate are 1 and 0 and so the output of the AND gate is ‘0’ (Minimum of 1 and 0). This is the input of NOT gate which gives the output $s=1$.

But the diagram states that ${{x}_{2}}=s$ i.e. $0=1$, a contradiction.

$\therefore$The output s is not uniquely defined. This type of circuit is not a combinatorial circuit.

Two combinatorial circuits : Circuit having inputs ${{x}_{1}},{{x}_{2}},......{{x}_{n}}$ and a single output are said to be combinatorial circuit if, the circuits receive the same input, they produce the same output i.e., if the input/output tables are identical.

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