NIMCET 2008 Question Paper with solutions

Question : 102 of 120

Marks: +1, -0

Identify the logic function performed by the circuit.

Solution:

f(x, y)=[\{x+x^{'} ⋅ y^{'}\}^{'}+\{x^{'} ⋅ y^{'}+y\}^{'}]^{'}

(by De Morgan's law)

=[x^{'} ⋅(x^{'} ⋅ y^{'})+(x^{'} ⋅ y)^{'} ⋅ y]^{'}

(by De Morgan's law)

=\{x^{'} ⋅(x+y)+(x+y) ⋅ y^{'}\}^{'} \;\;

(by De Morgan's law)

=\{x^{'} ⋅(x+y)\}^{'} ⋅\{(x+y) ⋅ y^{f}\}^{'} \;\;

(by Le Morgan's law)

=[x+(x+y)] ⋅[\{x+y⟩^{r}+y]

(by De Morgan's law)

=[x+x^{'} ⋅ y^{η} ⋅[x^{'}-y^{'}+y]

(by De Morgar's law)

=(x+x)(x+y^{3}+(x^{'}+y) ⋅(y^{'}+y)

(by Distributive law)

=1 ⋅(x+y) ⋅(x^{'}+y) ⋅ 1

(by Complement law)

=(x+y^{'}) ⋅(x^{'}+y)

(by Identity law)

=x ⋅ x^{'}+x y+y^{'} x^{'}+y Y

(by Distributive law)

=0+x y+y^{'} x^{'}+0

(by Complement law)

=x y+x^{'} y^{'}

(by Identity and Commutative law)
which represent exclusive NOR.

Go to Question:

Prev Question

Next Question