CSE GATE 2016 Question No 16 Digital Logic

Question No. 16 CSE | GATE 2016

Consider the Boolean operator # with the following properties:

$x\#0\;=\;x,\;x\#1\;=\;\overline x,\;x\#x\;=\;0\;and\;x\#\overline x\;=1.$ Then $ x#y $ is equivalent to

(A) $x\overset-y+\overset-xy$
(B) $x\overset-y+\overset-x\overset-y$
(C) $ \overline xy+xy $
(D) $xy+\overset-x\overset-y$

Answer : (A) $x\overset-y+\overset-xy$

GATE 2016 CSE Digital Logic Boolean Algebra

Solution of Question No 16 of GATE 2016 CSE Paper

x	y	x#y
0	0	0
0	1	1
1	0	1
1	1	0

$ \begin{array}{l}x\#0=x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...1\\x\#1=\overline x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...2\\x\#x=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...3\\x\#\overline x=1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...4\\x\#y=x\overline y+\overline xy\end{array} $

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GATE Papers >> CSE >> 2016 >> Question No 16

Answer : (A) $x\overset-y+\overset-xy$

Questions of Boolean Algebra

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