Related Articles

# GATE | Gate IT 2008 | Question 1

• Last Updated : 14 Feb, 2018

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

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.

Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up