1
GATE CSE 2015 Set 3
+2
-0.6
Given the function $$F = P′ + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$$ consider the following statements.

\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S1} \right)\,\,\,\,F = \sum {\left( {4,5,6} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S2} \right)\,\,\,\,F = \sum {\left( {0,1,2,3,7} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S3} \right)\,\,\,\,F = \sum {\Pi \left( {4,5,6} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S4} \right)\,\,\,\,F = \sum {\Pi \left( {0,1,2,3,7} \right)} \cr}

Which of the following is true?

A
$$(S1)$$- False, $$(S2)$$- True, $$(S3)$$- True, $$(S4)$$- False
B
$$(S1)$$- True, $$(S2)$$- False, $$(S3)$$- False, $$(S4)$$- True
C
$$(S1)$$- False, $$(S2)$$- False, $$(S3)$$- True, $$(S4)$$- True
D
$$(S1)$$- True, $$(S2)$$- True, $$(S3)$$- False, $$(S4)$$- False
2
GATE CSE 2015 Set 3
Numerical
+2
-0
The total number of prime implicants of the function
$$f\left( {w,x,y,z} \right) = \sum {\left( {0,2,4,5,6,10} \right)}$$ _________________.
3
GATE CSE 2015 Set 2
Numerical
+2
-0
The number of min-terms after minimizing the following Boolean expression is _______________ . $$\left[ {D' + AB' + A'C + AC'D + A'C'D} \right]'$$\$
4
GATE CSE 2015 Set 2
Numerical
+2
-0
A half adder is implemented with $$XOR$$ and $$AND$$ gates. A full adder is implemented with two half adders and one $$OR$$ gate. The propagation delay of an $$XOR$$ gate is twice that of an $$AND/OR$$ gate. The propagation delay of an $$AND/OR$$ gate is $$1.2$$ microseconds. A $$4$$-bit ripple-carry binary adder is implemented by using four full adders. The total propagation time of this $$4$$-bit binary adder in microseconds is____________ .