Modern Physics 6 Question 6

6. The logic gate equivalent to the given logic circuit is

(Main 2019, 9 April II)

(a) NOR

(b) NAND

(c) OR

(d) AND

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Solution:

  1. Truth table for given combination of logic gates is

$\boldsymbol{A}$ $\boldsymbol{B}$ $\boldsymbol{Y} _{\mathbf{1}}=\overline{\boldsymbol{A}}$ $\boldsymbol{Y} _{\mathbf{2}}=\overline{\boldsymbol{B}}$ $\boldsymbol{Y}=\overline{\boldsymbol{Y} _{\mathbf{1}} \cdot \boldsymbol{Y} _{\mathbf{2}}}$
0 0 1 1 0
1 0 0 1 1
0 1 1 0 1
1 1 0 0 1

Output $Y$ resembles output of an OR gate. So, given combination acts like an OR gate.

Alternate Solution

The given logic gate circuit can be drawn as shown below

Here,

$$ Y=\overline{Y _1 \cdot Y _2}=\overline{\bar{A} \cdot \bar{B}} $$

Using de-Morgan’s theorem, i.e.

$$ \begin{aligned} \overline{x \cdot y} & =\bar{x}+\bar{y} \\ \therefore \quad Y & =\overline{\bar{A}}+\overline{\bar{B}}=A+B \quad[\because \overline{\bar{x}}=x] \end{aligned} $$

This represents the boolean expression for OR gate.



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