GATE Digital Logic 3

Question 1

What is the output of the Boolean expression F = A·(A+B)?

Accepted Answer

A

Answer

By absorption law, A·(A+B) = A.

Question 2

A D flip-flop stores the value of D on which edge of the clock?

Accepted Answer

Rising edge

Answer

A positive-edge-triggered D flip-flop captures D on the rising (positive) edge of the clock.

Question 3

How many 2-to-4 decoders (with enable) are needed to build a 4-to-16 decoder?

Accepted Answer

5

Answer

One 2-to-4 decoder drives the enable of four 2-to-4 decoders, totaling 5 decoders.

Question 4

Which Karnaugh map grouping size is NOT valid when simplifying Boolean expressions?

Accepted Answer

3

Answer

K-map groups must be powers of 2 (1, 2, 4, 8, …); grouping 3 cells is invalid.

Question 5

The complement of (A+B)·C using De Morgan's theorem is:

Accepted Answer

A'·B'+C'

Answer

Applying De Morgan's twice: [(A+B)·C]' = (A+B)' + C' = A'·B' + C'.

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