GATE | Gate IT 2008 | Question 1

A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those. Which of the following sets of connectives is NOT functionally complete?
(A) EX-NOR
(B) implication, negation
(C) OR, negation
(D) NAND


Answer: (A)

Explanation:  

The EX-NOR is not functionally complete because we cannot synthesize all Boolean functions using EX-NOR gate only. This is primarily because we cannot obtain inverted output using EX-NOR. If we can obtain inversion from any gate then any logic function can be synthesized using that gate only.

NAND
(A.A)’ = A’+A’ = A’

OR and negation
(A+A)’ = A’.A’ = A’

Implication and negation
A->B = (A’+B)
Now if B is taken as negation of A then
A->A’ = A’+A’ = A’
Thus negation can be using these combinations of logics.

This solution is contributed by Kriti Kushwaha.

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