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7 votes
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Dual of EX-OR is equal to
(A) NAND
(B) NOR
(C) EX-NOR
(D) None of these

3 Answers

Best answer
18 votes
18 votes

EX-OR, A ⊕ B = ${A}'B + A{B}'$

Dual of EX-OR = $({A}'+B).(A+{B}')$ = ${A}'{B}'+AB$ = A⊙B = EX-NOR 

[Note :

Dual is different concept from Complement

In Dual, Replace AND with OR , OR with AND  and  replace 1's by 0's and 0's by 1's

In complement, In addition to above, we also replace Binary variables by its complement's, mean x by x' or x' by x.

In case of EX-OR , dual of EX-OR is same as its complement, but for different expression, it may differ. ]

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6 votes
6 votes

(AB')+(BA') dual is ((A'B)+(B'A))'

                             =((A'B)' . (B'A))'

                            =(A+B')(B+A')

                            =AB+A'B'  i.e. EX-NOR gate

if a function f(x)=f(x1 ,x2,........xn) then its dual will be f((x1)',(x2)',...............,(xn)')'

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answer = option D

its the Law of Duality which is applied on the entire equation/formula not on just an expression.
for more info check : http://math.stackexchange.com/questions/408409/duality-principle-in-boolean-algebra

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